Courses Offered by CATCO

A. Basic Courses

Research can be carried out by acquiring knowledge in one or more of the following areas.

  1. Use of Computers in Chemistry - Computational Chemistry
  2. Concepts and Models in Chemistry - Molecular Orbital Theory
  3. Quantum Chemistry, Basic Knowledge
  4. Computer Assisted Drug Design and Molecular Modeling

B. Advanced Courses

Depending on the area of research specialization knowledge has to be acquired in two or three advanced areas.

  1. Ab initio Methods I: Hartree-Fock Theory
  2. Ab initio Methods II: Electron Correlation Methods (CI and perturbation theory)
  3. Ab initio Methods III: Electron Correlation Methods (From Single to Multi-Configuration methods)
  4. Ab initio Methods IV: Electron Correlation Methods (Electron Pair and Coupled Cluster methods)
  5. Ab initio Methods V: Calculation of Molecular Properties
  6. Density Functional Theory
  7. Solution of Chemical Problems with Quantum Chemical Methods
  8. Elective Courses:

  9. Second Quantization
  10. Mathematics for Quantum Chemists
  11. Presentation Techniques in Chemistry - How to write a paper? How to give a seminar?
  12. Introduction into the use of quantum chemical programs.
  13. Symmetry and Group Theory
  14. Molecular Modeling and Drug Design
  15. Reaction Dynamics
  16. Time Dependent Methods
  17. Basic Quantum Mechanics
  18. Relativistic Methods
  19. Seminar Series in Theoretical Chemistry

In this connection, previous co-workers have specialized and have presented their knowledge in group seminars. Here are some seminar titles of the past years:

  1. GVB and GVB-MP2. Basic Theory and Application
  2. Second Quantization, Basics and Applications
  3. Relativistic Effects in Chemistry
  4. Representation of Projected Coupled Cluster Theory in the language of Second Quantization
  5. MO Description of Transition Metal Complexes
  6. Reaction Dynamics as Described with Adiabatic Modes and the Reaction Path Hamiltonian
  7. Coupled Cluster Theory with Singles and Doubles
  8. Theory of NMR Chemical Shifts

Basic Courses

  1. Computers in Chemistry - Computational Chemistry
    1. The course is structured into five parts:

    2. Facts on Computers and their use in Chemistry: history, development, architecture, and functioning of computers; hardware: from microchips and microprocessors to supercomputers; software: elements of machine language; computer languages; on-line use in analytical chemistry and spectroscopy; digitalization of measurements; curve smoothing; resolution enhancement; integration of signals, etc.
    3. The PC World: PC hardware; special software used in chemistry; text editing; analysis of data and data management; drawing of chemical structures; 3d-pictures of molecules; professional drawings; software for referencing; generation of data bases; expert software.
    4. Programming of a computer: elements of FORTRAN 90; FTN 90 is trained by writing 15 programs to solve problems such as calculation of pH values, concentration measurements or simulation of NMR spectra. Each problem is connected with a special mathematical method (integration, eigenvalue problem, etc.) and a summary is given where the same mathematical problem may turn up in chemistry.
    5. Computational Chemistry I:Computer assisted structure elucidation; Chemometrics; Computer assisted synthesis; artificial intelligence; special data bases; CAS-ONLINE.
    6. Computational Chemistry II:From force fields to molecular simulations; molecular modeling; quantum chemistry: from semiempirical to correlation corrected ab initio methods; how to use a supercomputer; strategies for programming of large programs with 100 000 and more statements.

    The main part of the practical work consists of working with computers of different type. All parts of the practical work are compulsory:

    1. PC laboratory: 3 problems have to be solved for each of the following topics: text editing, data analysis, data management; drawing of chemical structures, 3d-representation of molecules; generation of figures, creating and using data bases. At the end, a manuscript with figures, schemes, diagrams, tables, and reference list has to be prepared with professional layout.
    2. Programming of computers: ca. 20 FTN 90 programs (from 30 to 300 lines) are written to solve problems from chemistry. Emphasis is laid on a systematic approach to the problem within the following strategy: 1) translation of the chemical problem into mathematical language; 2) flow chart of a FTN program; 3) programming of a test version; 4) debugging and testing; 5) improving the program; 6) documentation of the program.
    3. Use of Networks: The student learns how to use networks to get access to other computers. In this connection, basic features of CAS-ONLINE are explained and up to three literature searches are performed.
    4. Use of supercomputers: Semiempirical and ab initio programs (MOPAC, GAUSSIAN) are used to carry out about 6 illustrative calculations (determination of geometry, heat of formation, relative energy, ionization potential, dipole moment, charge distribution, etc.).
    5. Excursion: The supercomputer center is visited and a guided tour of the CRAY YMP is made. A one-day minisymposium on supercomputing is organized by experts of the supercomputer center.
  2. Concepts and Models in Chemistry - MO Theory
    1. Atomic and Molecular orbitals (basic facts from MO theory; representation of orbitals; energy diagrams; LCAO-MO approach).
    2. Theory of the Chemical Bond (MO description of the bond; electron density description; quantum mechanical description; orbital overlap; bonding in diatomic molecules; electronegativity and bond polarity; PE spectroscopy).
    3. Structure of Molecules (Principle of maximum overlap; hybridization; bond orbitals; VSEPR model; the direct valence model).
    4. Mulliken-Walsh MO model (Walsh diagrams for AHn (n = 2,3,4), HAB, H2AB, HnAAHn (n=1,2,3) molecules).
    5. PMO Model (basic formulas; 1,2,3,4-electron cases; first and second order Jahn-Teller effects).
    6. Hückel MO model (s-p-separation; Hückel theory; aromaticity concept).
    7. Classical Mechanics applied to chemistry (concepts of strain; molecular mechanics; heats of formation from group increments; molecular modeling).
    8. Interactions between orbitals (hyperconjugation; anomeric effect; through-space and through-bond interactions; homoconjugation and homoaromaticity; spiroconjugation).
    9. Conformation and configuration of molecules (Rotational potential of single rotor molecules; fourier expansion of potential; electronic effects that determine rotational potential; steric repulsion and steric attraction; cis-effect).
    10. Theory of Pericyclic reactions (The Woodward-Hoffmann rules: orbital symmetry analysis; cycloadditions; electrocylic reactions; sigmatropic rearrangements; cheletropic reactions).
    11. Evans-Dewar-Zimmermann concept (Evans principle; hückel and Möbius systems; Dewar-Zimmermann rules)
    12. Hypervalent Molecules (orbitals and bonding; pseudorotation in AH5).
    13. Transition metal chemistry: Basic Facts and Important Terms (nomenclature; role of transition metal complexes in chemical industry; generalized MO diagrams and electron counting rules).
    14. ML6, ML5 and ML4 Complexes (octahedral ML6 complexes; high spin and low spin complexes; square planar and tetrahedral ML45n complexes in Biochemistry).
    15. MLn Fragments (Lego-principle of MO diagrams; ML2, ML3, ML4, and ML5 fragments and their orbitals).
    16. MCp and MCp2 Complexes (CpML3 complexes; CpM fragment orbitals; metallocenes).
    17. The isolobal Analogy (isolobal fragments; cluster orbitals; capped annulenes; Wade rules).
  3. Applied Quantum Chemistry
    1. Early Quantum Theory: historical overview; influence of physics on Theoretical Chemistry; blackbody radiation; photoelectric effect; Bohr and the H atom; de Broglie wavelength; Heisenberg uncertainty principle.
    2. The wave equation: differential equations; separation of variables.
    3. The Schrödinger equation and simple applications such as the particle in the box.
    4. Basic Quantum Mechanics: state of a system; operators and observables; postulates and general principles of quantum mechanics.
    5. The Harmonic oscillator: diatomic molecules; solution of the harmonic oscillator problem; quantum mechanical tunneling.
    6. From one to three dimensions: particle in the 3-dimensional box; the rigid rotator; the hydrogen atom; quantum numbers; orbitals.
    7. Approximated methods: independent particle approximation; variational method; perturbation theory.
    8. Calculation of atoms: application of variational method and perturbation theory to the He atom; Hartree-Fock calculation of the He atom; electron spin and Pauli principle; antisymmetric wave functions and slater determinants; singlet and triplet wave functions; atomic term symbols.
    9. Calculation of molecules: VB theory of H2; chemical bonding; MO theory of H2+ and H2; improvement of VB theory; GVB; configuration interaction (CI); CID and CISD.
    10. Hartree-Fock theory: Fock operator; HF equations; LCAO-ansatz; Roothaan-Hall equations; SCF.
    11. Ab initio theory: STF and GTF; basis sets; RHF and UHF; electron correlation; CI, MBPT, CC, MCSCF.
    12. Semiempirical methods: p-methods; Valence electron methods: extended Hückel; NDO methods; CNDO, INDO, MINDO, MNDO, AM1, PM3; use of semiempirical methods.
  4. Computer Assisted Drug Design and Molecular Modeling
    1. Drug Discovery and Drug Design
      1. 1.1
        What is a drug?
      2. 1.2
        The role of drugs in the practice of medicine
      3. 1.3
        The role of Pharmaceutical Chemistry
      4. 1.4
        The history of Pharmaceutical Chemistry
      5. 1.5
        Natural substances as drugs, Opium, Quinine, Glycosides, Aspirin, Alkaloids
      6. 1.5.1
        Paradigm shifts in medicine
      7. 1.6
        Modern drug design: What requirements must a drug fulfill?
      8. 1.7
        Stages and cost of modern drug design
      9. 1.8
        Tools and teams in modern drug design
      10. 1.9
        The role of Computational Chemistry in drug design
      11. 1.11
        Drug Discovery - Filtering out Failures
      12. 1.12
        Advertisements in the area of CADD
    2. Computer Assisted Drug Design (CADD)
      1. 2.1
        What is CADD? - Explanation of some basic terms
      2. 2.2
        Pharmacophore, Lock-Key principle and induced fit theory
      3. 2.2.1
        100 years of the Lock-Key Principle
      4. 2.2.2
        The Lock-key Principle and the Induced Fit Theory
      5. 2.2.3
        The nature of pharmacophores
      6. 2.2.4
        Molecular Flexibility
      7. 2.2.5
        Identification of pharmacophores
      8. 2.2.6
        Searching for pharmacophores
      9. 2.3
        Molecular Recognition and Molecular Docking
      10. 2.4
        What makes a compound bioactive?
      11. 2.5
        The objects of CADD and Molecular Modeling
      12. 2.6
        What are the driving forces of Receptor-Drug interactions?
      13. 2.7
        Solvent modeling - the role of water
      14. 2.7.1
        Properties of water
      15. 2.7.2
        Water as a solvent: Aqueous solutions
      16. 2.7.3
        Hydrophilic compounds
      17. 2.7.4
        Hydrophobic compounds
      18. 2.7.5
        Amphiphatic compounds
      19. 2.8
        The dynamic aspect of modeling
      20. 2.9
        How did CADD develop?
      21. 2.10
        What are the techniques and concepts used in CADD and Molecular Modeling?
      22. 2.11
        Disciplines and fields contributing to CADD and Molecular Modeling
    3. Molecular Mechanics (MM)
      1. 3.1
        Basic considerations concerning force fields
      2. 3.1.1
        Spectroscopic force fields
      3. 3.1.2
        The diatomic case
      4. 3.1.3
        Vibrations of polyatomic molecules
      5. 3.2
        The concept of the force field in MM: historical development
      6. 3.3
        Transferability of force fields
      7. 3.4
        The energy expression in MM
      8. 3.4.1
        Bond stretching potential
      9. 3.4.2
        Angle bending potential
      10. 3.4.3
        Inversion or out-of-plane bending potential
      11. 3.4.4
        Inversion or out-of-plane bending potential
      12. 3.5
        Non-bonded interaction potential
      13. 3.5.1
        Electrostatic interaction potentials
      14. 3.5.2
        Interaction between bond dipole moments
      15. 3.5.3
        Calculation of electrostatic interactions
      16. 3.5.4
        How to get partial charges?
      17. 3.5.4.1
        Charges from electronegativities (Sanderson)
      18. 3.5.4.2
        Gasteiger-Marsili charges
      19. 3.5.4.3
        Charges from Molecular Dipole moments
      20. 3.5.4.4
        Charges from quantum chemical calculations
      21. 3.5.5
        Dispersion and exchange repulsion interactions
      22. 3.5.6
        Model potentials for van der Waals interactions
      23. 3.5.7
        Spherical and non-spherical atoms
      24. 3.5.8
        The van der Waals (vdW) radius
      25. 3.5.9
        Parametrization of vdW potentials
      26. 3.6
        H-bonding
      27. 3.6.1
        H-bonding potentials
      28. 3.7
        Cross term potentials
      29. 3.7.1
        Stretch-bend cross term potential
      30. 3.7.2
        Other cross term potentials
      31. 3.8
        Parametrization of a Force Field
      32. 3.8.1
        Parameter optimization
      33. 3.9
        Force field energies V
      34. 3.9.1
        Some Basic considerations Concerning Energies
      35. 3.9.2
        Molecular Mechanics Calculation of heats of formations
      36. 3.10
        Determination of energy and geometry
      37. 3.10.1
        Newton-Raphson Method
      38. 3.10.2
        Quasi-Newton Methods; Davidon-Fletcher-Powell
      39. 3.10.3
        Steepest descent method
      40. 3.10.4
        Conjugate gradient method
      41. 3.10.5
        Univariate Search Method
      42. 3.10.6
        Overview over Optimization Methods
      43. 3.11
        Differences between spectroscopic and MM force fields
      44. 3.12
        Classification of force fields
      45. 3.13
        List of force fields presently in use
      46. 3.14
        Generic Force Fields
      47. 3.15
        Treatment of long range Coulomb Forces
      48. 3.16
        Applicability and limitations of a MM approach
      49. 3.17
        Extension of MM; Description of p-conjugated molecules
      50. 3.18
        QM/MM methods
      51. 3.18.1
        How does a QM/MM method work?
      52. 3.18.2
        The junction between the QM and MM regions
      53. 3.18.3
        Implementation of the QM/MM approach
      54. 3.18.4
        Applications of QM/MM
    4. Simulation of Macroscopic Properties
      1. 4.1
        Basic terms from statistical mechanics
      2. 4.1.1
        Concept of the ensemble
      3. 4.1.2
        Collection of formulas
      4. 4.2
        Searching phase-space and generating an ensemble
      5. 4.2.1
        Overview over methods
      6. 4.2.2
        Systematic search methods
      7. 4.3
        Monte Carlo (MC) methods (Random Methods I)
      8. 4.3.1
        Monte Carlo Integration: Hit and Miss
      9. 4.3.2
        Random number generators
      10. 4.3.3
        Sample mean integration
      11. 4.3.4
        Importance sampling
      12. 4.3.5
        Sampling error
      13. 4.3.6
        Metropolis MC method
      14. 4.4
        Random methods without V: Distance Geometry and NMR Spectroscopy (Random methods II)
      15. 4.4.1
        Nuclear Overhauser Effect (NOE)
      16. 4.4.2
        Karplus Curves and NMR spin-spin coupling constants
      17. 4.4.3
        Basic considerations concerning DG
      18. 4.4.3.1
        Distance constraints
      19. 4.4.3.2
        DG methods: Embedding and metric matrix method
      20. 4.4.3.3
        The Metric Matrix method
      21. 4.4.3.4
        Triangle Inequality Bounds Smoothing
      22. 4.4.3.5
        Metrization
      23. 4.4.3.6
        Refinement
      24. 4.4.3.7
        Chiral constraints and the chiral error function
      25. 4.4.3.8
        Four-dimensional refinement
      26. 4.4.3.9
        Minimization
      27. 4.5
        MD simulation methods
      28. 4.5.1
        Basic considerations
      29. 4.5.2
        Practical Aspects of a MDS calculation
      30. 4.5.2.1
        Choosing the initial configuration
      31. 4.5.2.2
        Choosing the time step
      32. 4.5.2.3
        Choosing the initial velocities
      33. 4.5.2.4
        Checking the MDS calculation
      34. 4.5.2.5
        Checking equilibration
      35. 4.5.3
        Verlet method
      36. 4.5.4
        Leapfrog method
      37. 4.5.5
        Constrained Verlet: SHAKE method
      38. 4.5.6
        Different types of MDS
      39. 4.5.7
        Constant-T methods
      40. 4.5.7.1
        Weak coupling methods
      41. 4.5.8
        Constant-P methods
      42. 4.5.8.1
        Weak coupling methods
      43. 4.5.9
        Stochastic dynamic simulations
      44. 4.5.10
        Boundary conditions
      45. 4.5.10.1
        Vacuum boundary conditions
      46. 4.5.10.2
        Periodic boundary conditions
      47. 4.5.10.3
        Extended wall region boundary conditions
      48. 4.5.11
        Quantities calculated
      49. 4.5.12
        Radial Distribution function
      50. 4.5.13
        Calculation of time-dependent properties
      51. 4.5.14
        History of MDS
      52. 4.6
        Calculation of the Free energy
      53. 4.6.1
        Why is it difficult to calculate A, G, and S?
      54. 4.6.2
        The coupling parameter approach
      55. 4.6.3
        The Thermodynamic perturbation method
      56. 4.6.4
        The Thermodynamic integration method
      57. 4.6.5
        The potential of mean force
      58. 4.6.6
        Free energy differences and the thermodynamic cycle
      59. 4.6.7
        Beyond the free energy: Entropy and enthalpy
      60. 4.6.8
        Practical considerations
      61. 4.6.9
        Recommendations
    5. Molecular Modeling and Molecular Graphics
      1. 5.1
        Historical overview
      2. 5.2
        Development of computer graphics
      3. 5.3
        Graphical representation of molecules: Standard models
      4. 5.4
        Graphical representation technologies
      5. 5.5
        Simplified molecular representations
      6. 5.6
        Molecular surfaces and volumes
      7. 5.6.1
        Corey-Pauling-Koltun (CPK) or van der Waals surface
      8. 5.6.2
        The Solvent accessible surface (SAS)
      9. 5.6.3
        Solvent excluded surface - Conolly surface
      10. 5.6.4
        Surfaces of macromolecules
      11. 5.6.5
        The electron density surface
      12. 5.6.6
        Channel surface and separating surface
      13. 5.7
        Molecular volume
      14. 5.7.1
        Packing defects in the protein interior
      15. 5.7.2
        Voroni Polyhedra (Dirichlet cells): Protein packing density
      16. 5.8
        Molecular superposition and molecular similarity
      17. 5.8.1
        Manual approach (Flexible superposition)
      18. 5.8.2
        Atom based methods (DISCO and SQ)
      19. 5.8.3
        Molecular similarity: Field based methods
      20. 5.9
        Molecular skin
      21. 5.10
        Mapping of information on molecular surfaces
      22. 5.10.1
        The lipophilicity potential
      23. 5.10.2
        The electrostatic potential
      24. 5.11
        Molecular shape descriptors
      25. 5.11.1
        Surface Topology Index
      26. 5.11.2
        Flexibility of the surface
      27. 5.12
        Examples of modern molecular graphics
    6. Conformational Analysis
      1. 6.1
        Conformations of biomacromolucules
      2. 6.1.1
        Primary, secondary, tertiary, and quaternary structure of proteins
      3. 6.1.2
        Details of Protein structure (Appendix to 6.1.1)
      4. 6.2
        Systematic search methods
      5. 6.2.1
        Tree search methods
      6. 6.2.2
        Model-building approaches
      7. 6.3
        Random search methods
      8. 6.3.1
        Genetic algorithms
      9. 6.3.2
        Distance geometry
      10. 6.3.3
        Metropolis Monte Carlo
      11. 6.4
        MDS-based methods
      12. 6.4.1
        Simulated annealing (SA)
      13. 6.4.2
        Structure refinement by simulated annealing
      14. 6.4.3
        Crystallographic refinement
      15. 6.4.3.1
        Structure factor and electron density
      16. 6.4.4
        NMR structure refinements
    7. Chemometrics
      1. 7.1
        Orgin and current status
      2. 7.2
        Multivariate Data
      3. 7.2.1
        Definitions
      4. 7.2.2
        Organization and classification of data
      5. 7.2.3
        Preprocessing
      6. 7.2.4
        Distances between objects
      7. 7.2.5
        Latent variables
      8. 7.3
        Linear Methods
      9. 7.3.1
        Projection of multivariate data
      10. 7.3.2
        Principal component analysis (PCA)
      11. 7.3.3
        Multiple linear regression (MLR) and principle component regression (PCR)
      12. 7.3.4
        Partial least squares method (PLS)
      13. 7.4
        Non-linear methods
      14. 7.4.1
        An example for non-linear models
      15. 7.5
        Modeling methods
      16. 7.5.1
        SIMCA principle component modeling
      17. 7.5.2
        Classification methods
      18. 7.5.2.1
        Probability density classification (Bayes strategy)
      19. 7.5.2.2
        K nearest-neigbor classification (KNN)
      20. 7.5.3
        Factor analysis
      21. 7.5.4
        Cluster analysis
      22. 7.5.5
        Linear discriminant analysis (LDA)
      23. 7.6
        Validation tools
      24. 7.6.1
        Cross-validation
      25. 7.6.2
        Bootstrapping
      26. 7.6.3
        Frequently used statistical indices
      27. 7.6.4
        Cross-validation in PLS
      28. 7.6.5
        Chance effects and chance correlation
    8. Artificial Neural Networks (ANN)
      1. 8.1
        Background and basics of ANN
      2. 8.2
        What can neural networks do?
      3. 8.2.1
        Artificial neuron
      4. 8.2.2
        Net input, net and weight
      5. 8.2.3
        How to get the best weights?
      6. 8.2.4
        Transfer functions in neurons
      7. 8.2.5
        Bias
      8. 8.2.6
        Linking neurons to networks
      9. 8.3
        Architecture
      10. 8.4
        The Kohonen network
      11. 8.4.1
        Special characteristics
      12. 8.4.2
        Competitive learning
      13. 8.4.3
        An example: mapping from 3 to 2 dimensions
      14. 8.4.4
        Summary
      15. 8.5
        Counterpropagation
      16. 8.5.1
        Supervised competitive learning
      17. 8.5.2
        Summary
      18. 8.6
        Error-backpropagation learning
      19. 8.6.1
        Architecture
      20. 8.6.2
        Learning by back propagation
      21. 8.6.3
        Learning algorithm
      22. 8.6.4
        Essentials
      23. 8.7
        When is the training finished?
      24. 8.7.1
        Overtraining
      25. 8.8
        Applications of ANNs in Drug design
      26. 8.8.1
        ANN in Quantitive structure activity relationships
      27. 8.8.2
        ANN to determine the secondary structure of proteins
      28. 8.8.3
        Kohonen maps of the electrostatic potential
    9. Lipophilicity
      1. 9.1
        Factorization of molecular lipophilicity
      2. 9.2
        1D-approaches for calculating partition coefficients
      3. 9.2.1
        Substituent constants of Hansch and Fujita
      4. 9.3
        2D-appraoches for calculating partition coefficients
      5. 9.3.1
        Methods based on fragmental constants and correction factors
      6. 9.3.2
        Method of Leo and Hansch (CLOGP)
      7. 9.3.3
        Klopman's method (CASE)
      8. 9.3.4
        Methods based on fragmental constants only
      9. 9.3.4.1
        Method of Suzuki and Kudo (CHEMICALC)
      10. 9.3.4.2
        Method of Broto, Moreau and Vandycke (ALOGP)
      11. 9.3.5
        Methods based on global two-dimensional structural properties
      12. 9.3.5.1
        Calculation of peptide lipophilicity
      13. 9.3.5.2
        Calculation of lipophilicity using structural parameters
      14. 9.4
        3D- approaches for calculating partition coefficients
      15. 9.4.1
        Solvent-accessible surface areas (SASA)
      16. 9.4.2
        MO calculations and Bodor's method (BLOGP)
      17. 9.4.3
        Methods based on molecular fields: the lipophilicity potential (MLP)
      18. 9.5
        4D- approaches for calculating partition coefficients
      19. 9.5.1
        Methods based on an ensemble of conformers
      20. 9.5.2
        Methods based on direct computation
      21. 9.5.3
        Methods based on a continuum solvation model
      22. 9.5.4
        Methods based on free energy perturbation methods
      23. 9.6
        Comparison of the accurary of different methods
      24. 9.7
        Examples from drug design
      25. 9.7.1
        log P as a tool to unravel intramolecular interactions
      26. 9.7.2
        log P values in 2D-QSAR
      27. 9.8
        Summary of computer programs
      28. 9.9
        Concluding remarks
    10. 2D-Quantitative Structure-Activity Relationship (2D-QSAR)
      1. 10.1
        Definition
      2. 10.2
        QSAR methodology
      3. 10.2.1
        Historical background
      4. 10.3
        Basic concepts of QSAR
      5. 10.3.1
        Hansch analysis
      6. 10.3.2
        Free-Wilson analysis
      7. 10.3.3
        An example: Adrenergic activities of N,N-di-methyl-a bromopheneythlamines
      8. 10.3.4
        Summary
      9. 10.4
        Molecular descriptors
      10. 10.4.1
        Electronic parameters
      11. 10.4.2
        Polar interactions
      12. 10.4.3
        Steric parameters
      13. 10.4.4
        Topological parameters
      14. 10.4.5
        Quantum-chemical descriptors
      15. 10.5
        Biological parameters
      16. 10.6
        2D-QSAR in drug design
      17. 10.6.1
        Transport and distribution of drugs in biological systems
      18. 10.6.2
        Enzyme inhibition
      19. 10.6.3
        Model system for cysteine protease
      20. 10.6.4
        Prediction of mutagenic potencies
      21. 10.6.5
        QSAR for antimalarical compounds
      22. 10.6.6
        b1- and b2- antagonist activities
      23. 10.6.7
        Activity-activity relationships
      24. 10.7
        Validation of QSAR models
      25. 10.8
        Conclusions
    11. 3D-QSAR; Comparative Molecular Field Analysis (CoMFA) and - Similarity Analysis (CoMSIA)
      1. 11.1
        3-QSAR
      2. 11.2
        Assumptions in 3D-QSAR
      3. 11.3
        CoMFA methodology
      4. 11.4
        Steps of a CoMFA analysis
      5. 11.4.1
        Pharmacophore hypothesis and alignment
      6. 11.4.2
        Superposition of all molecules
      7. 11.4.3
        Box, Grid size and 3D field calculations
      8. 11.4.4
        CoMFA Data Table
      9. 11.4.5
        Derivation of the CoMFA model
      10. 11.4.6
        CoMFA coefficient maps
      11. 11.4.7
        Validation of results
      12. 11.5
        An example: CBG and TBG binding affinities of steroids
      13. 11.6
        CoMFA application in drug design, overview
      14. 11.7
        Conclusions on CoMFA
      15. 11.8
        Comparative molecular similarity analysis (CoMSIA)
      16. 11.8.1
        Definition of similarity indices
      17. 11.8.2
        Similarity fields
      18. 11.9
        An example benzamidine inhibitors binding to trypsin, thrombin, and factor Xa
    12. CADD: Methods and Strategies
      1. 12.0.1
        The drug development process (target oriented)
      2. 12.1
        Lead discovery
      3. 12.2
        Irrational drug design and combinatorial chemistry
      4. 12.2.1
        The combinatorial explosion of chemistry
      5. 12.2.2
        What is combinatorial chemistry
      6. 12.2.3
        Merrifield's synthesis of peptides
      7. 12.2.4
        CombChem: Mix-and-split libraries
      8. 12.2.5
        Historical development of CombChem
      9. 12.3
        Virtual screening
      10. 12.3.1
        Setting up a virtual library
      11. 12.3.2
        Practical considerations: Encoding of the library
      12. 12.3.3
        The virtual screening process
      13. 12.3.4
        2D-similarity: Tanimoto coefficients
      14. 12.3.5
        Clustering (=pooling) of structures
      15. 12.3.6
        Virtual screening: 3D similarity
      16. 12.3.7
        Reduction and diversity of a virtual library
      17. 12.3.8
        Data mining
      18. 12.4
        Structure-based ligand design: Pharmacophore generation
      19. 12.4.1
        Structure-based ligand design
      20. 12.4.2
        Determination of a pharmacophore
      21. 12.4.3
        The active analog approach (AAA)
      22. 12.4.4
        Ensemble distance geometry
      23. 12.4.5
        Ensemble molecular dynamics
      24. 12.4.6
        Pharmacophores by clique detection
      25. 12.4.7
        Pharmacophore representation
      26. 12.5
        Molecular recognition
      27. 12.6
        Molecular docking
      28. 12.7
        De Novo design of ligands
      29. 12.7.1
        Analysis of the receptor: Generation of a constraints model
      30. 12.7.1.1
        The GRID program
      31. 12.7.1.2
        The Multiple-Copy Simultaneous Search (MCSS) method
      32. 12.7.1.3
        The Program LUDI
      33. 12.7.2
        Structure generation methods
      34. 12.7.2.1
        The outside-in (linking) approach: LUDI
      35. 12.7.2.2
        The linking part
      36. 12.7.2.3
        Creating real molecules
      37. 12.7.2.4
        The inside-out (building) approach: GROW
      38. 12.7.2.5
        Program LEGEND
      39. 12.7.3
        Structure evaluation
      40. 12.7.4
        When does one use de Novo design?
      41. 12.7.5
        Practical advice on the application of de Novo design methods
      42. 12.7.6
        De Novo design: Conclusions and future perspectives
      43. 12.8
        Petides and peptide analogs as drugs: Peptidomimetics
      44. 12.8.1
        Peptidomimetics
      45. 12.8.2
        Design of peptidomimetics: the CAVEAT program
    13. Protein Modeling
      1. 13.1
        The Protein Data Bank (PDB)
      2. 13.2
        Relationship between sequence and 3D structure of a protein
      3. 13.3
        Alignment of protein sequences
      4. 13.3.1
        Needleman-Wunsch alignment method
      5. 13.3.2
        Multiple sequence alignments (MSA)
      6. 13.3.2.1
        Construction of the core
      7. 13.3.2.2
        Construction of loops and turns
      8. 13.3.2.3
        Construction of the Side chains
      9. 13.3.2.4
        Refinement of the homology model
      10. 13.4
        Homology modeling of proteins
      11. 13.5
        Prediction of protein structures by threading
      12. 13.6
        Comparison of various strategies in homology modeling
      13. 13.7
        Protein folding
      14. 13.7.1
        Thermodynamics of protein folding
      15. 13.7.2
        Levinthal's paradox and the kinetics of protein folding
    14. Present and Future Perspectives of Drug Design
      1. 14.1
        Successes of CADD
      2. 14.2
        Genetechnology and drug design
      3. 14.3
        Bioinformatics
      4. 14.4
        Future developments
      5. 14.4.1
        Improvements of force fields
      6. 14.4.2
        Integration of quantum chemical methods, better QC/MM methods
      7. 14.4.3
        Better methods for DG calculations
      8. 14.4.4
        ADME modeling
  5. Ab initio Methods I: Hartree-Fock Theory
    1. Introduction
    2. Definition of the term ab initio, goals; advantages; size-extensivity, approximations involved; limitations, classification; difference between empirical, semiempirical, and nonempirical methods; What is calculated? Comparison with experimental measurements; acronyms; units; conventions; history.

      1. 1.1
        What are ab initio calculations?
      2. 1.2
        Goals of ab initio quantum chemistry
      3. 1.3
        Criteria for ab initio methods
      4. 1.4
        Approximations and limitations
      5. 1.5
        What is calculated?
      6. 1.6
        Classification of methods used in Computational Chemistry
      7. 1.7
        Acronyms, units, symbols
      8. 1.8
        History of ab initio Quantum Chemistry
      9. 1.9
        What ab initio programs are available
      10. 1.10
        What ab initio programs are available
    3. The independent particle model
    4. Unitary vector space, Hilbert space, basis vectors; scalar product, operators, dyadic product, projection operator, Hermitian operator, turn-over rule, unitary operator, eigenvalue problem, Hamilton operator; Born-Oppenheimer approximation, single determinant wave-function, what is an orbital? spin orbitals and space orbitals; Variational principle, Hartree product; antisymmetry principle, Slater determinant; matrix elements for Slater determinants; Slater-Condon rules, exchange and Coulomb operator, Fock operator, Hartree-Fock equations; canonical form, orbital energy, separation of spin, energy for closed-shell system, restricted HF (RHF), LCAO approach; basis functions, metric of a non-orthogonal basis, overlap integrals, Fock matrix, Roothaan-Hall equations, energy expressions, density matrix.

      1. 2.1
        Some useful basics from quantum mechanics
      2. 2.2
        The independent particle model
      3. 2.3
        Hartree product versus Slater determinant
      4. 2.4
        Determination of the normalization constant
      5. 2.5
        Matrix Elements over Slater determinants - Slater-Condon rules
      6. 2.5.1
        One electron operators
      7. 2.5.2
        Two electron operators
      8. 2.6
        Simplification of the Hamiltonian to an effective One-electron operator
      9. 2.6.1
        Hartree Fock (HF) energy formula
      10. 2.7
        Hartree Fock Equations
      11. 2.8
        LCAO-Ansatz to solve the HF equations - Roothaan-Hall equations
      12. 2.9
        Calculation of the energy according to Roothaan-Hall
    5. What is needed for a Hartree-Fock (HF) calculation?
    6. Flow chart for ab initio calculations; input; choice of the coordinates; Cartesian and internal coordinates, geometry optimization and the right choice of coordinates, z-matrix formalism; dummy atoms; puckering coordinates; determination of symmetry, number of independent internal coordinates, molecular framework group, what ab initio programs are available? How to get them; how to use them?

      1. 3.1
        Flow chart for a HF calculation
      2. 3.2
        Input for a HF calculation
      3. 3.2.1
        Specification of the molecule
      4. 3.2.2
        Molecular geometry
      5. 3.2.2.1
        Cartesian versus internal coordinates
      6. 3.2.2.2
        The z-matrix formalism
      7. 3.2.2.3
        Special coordinates - puckering parameters
      8. 3.3
        How to find the right number of coordinates?
      9. 3.3.1
        Determination of molecular point group in an ab initio program
      10. 3.3.2
        Number of independent coordinates for symmetric molecules
      11. 3.4
        The molecular framework group
      12. 3.5
        What ab initio programs are available?
    7. The basis functions
    8. Building-block principle, H-type functions and H-type orbitals; Slater-type functions and Slater-type orbitals; the exponent zeta; diffuse and compact basis functions, Slater rules; Gaussian-type functions and Gaussian-type orbitals, cusp problem, energy of the H atom; LCGTF, difference between STFs and GTFs, cartesian Gaussians; advantages and disadvantages; first order and second order GTF, the index l, Gaussian lobe functions.

      1. 4.1
        The building block principle of MO theory
      2. 4.2
        Hydrogen type functions and Hydrogen type orbitals
      3. 4.3
        Slater type functions (STF) and Slater type orbitals (STO)
      4. 4.4
        Slater rules for zeta values
      5. 4.5
        Gaussian type functions (GTF) and Gaussian type orbitals (GTO)
      6. 4.5.2
        Energy of the ground state of H
      7. 4.5.3
        Comparison of HF, Slater, and Gaussian orbitals
      8. 4.5.4
        Cartesian Gaussian functions
      9. 4.5.5
        Gaussian lobe functions
      10. 4.6
        Summary
    9. The basis set
    10. Notation; minimal zeta basis; double zeta basis; choice of the exponent, split valence basis, extended basis sets; isotropic limit, HF limit, augmented basis sets; hidden variables; floating functions; bond functions; polarization functions (p, d, f, g, h); radial and angular polarization, notation for augmented basis sets, weight, size, and position of a basis function, uncontracted and contracted basis sets; construction of contracted basis sets; contraction criteria; segmented and generalized contraction, the scaling theorem; notation; Huzinaga-Dunning basis sets; Pople minimal basis sets; shell constraints; STO-NG; split valence basis sets, augmented split valence basis sets; addition of diffuse functions; even-tempered basis sets, selection of a basis set, Pople's recipe, basis sets for special molecular properties, Dunning basis sets.

      1. 5.1
        How to use basis functions?
      2. 5.2
        Notation for basis sets
      3. 5.3
        Minimal basis sets (MBS, SZ)
      4. 5.4
        Double Zeta basis sets (DZ)
      5. 5.5
        Split-valence basis sets (VDZ)
      6. 5.6
        Extended Basis sets: TZ, QZ, PZ
      7. 5.7
        Augmented basis sets
      8. 5.7.1
        Floating basis functions
      9. 5.7.2
        Bond functions
      10. 5.7.3
        Polarization functions
      11. 5.8
        Uncontracted and contracted basis sets
      12. 5.8.1
        Contraction of a (7s3p) basis for N
      13. 5.8.2
        Notation for contracted basis sets
      14. 5.8.3
        Rules for getting contracted basis sets
      15. 5.8.4
        General contraction schemes
      16. 5.9
        Pople's minimal basis sets
      17. 5.9.1
        Scaling theorem
      18. 5.9.2
        STO-NG minimal basis sets
      19. 5.10
        Pople's split valence and augmented split valence basis sets
      20. 5.11
        Special Basis sets
      21. 5.11.1
        Augmented basis sets with diffuse functions
      22. 5.11.2
        Even-tempered basis sets
      23. 5.12
        Selection of an appropriate basis set for a given problem
      24. 5.12.1
        What is available?
      25. 5.12.2
        How to select a basis set?
      26. 5.12.3
        Pople's recipe
      27. 5.12.4
        How to get basis sets for high accuracy calculations?
      28. 5.12.5
        What basis set is needed for what property?
    11. Calculation of integrals
    12. Single bar and double bar integrals, physical and chemical notation of integrals; number of integrals; shell structure; one-electron integrals; overlap integrals, Cartesian Gaussian functions, spherical Gaussians, transformation from cartesian to spherical Gaussians, angular shell, contaminants, Gaussian product theorem, Laplace transform of r12-1, incomplete Gamma functions, shift of angular momentum, differentiation of Gaussian functions, recurrence relationships, Cartesian Hermite Gaussian-type functions, translational invariance, Gaussian Quadrature, overlap integrals, kinetic energy integrals, nucleus-electron attraction integrals, two-electron repulsion integrals (ERIs), [ss|ss] ERI, prescreening of ERIs, McMurchie-Davidson scheme, Dupuis-King-Rys scheme, Rys polynomials, Pople-Hehre scheme, exponent sharing, early contraction, late contraction, axes rotation, PRISM algorithm, contraction and scaling, choice diagrams, Obara-Saika scheme, Resolution of the identity (RI) method, canonical ordering, sequential and random storing, batch processing, packing and unpacking of ERI labels, synchronous/asynchronous IO, buffering of ERIs.

      1. 6.1
        Notation for electron integrals
      2. 6.2
        Number of integrals
      3. 6.3
        Properties of GTFs relevant for integral calculations
      4. 6.3.1
        Basics
      5. 6.3.2
        Gaussian Product Theorem
      6. 6.3.3
        The Laplace Transform of r12-1
      7. 6.3.4
        The Transfer equation
      8. 6.3.5
        Differentiation and recurrence relationships
      9. 6.3.6
        Gaussian Quadrature
      10. 6.4
        Overlap integrals
      11. 6.5
        Kinetic energy integrals
      12. 6.6
        Nucleus-electron attraction integrals
      13. 6.7
        Evaluation of two-electron repulsion integrals (ERIs)
      14. 6.7.1
        Evaluation of the [ss|ss] ERI
      15. 6.7.1.1
        Prescreening of ERIs
      16. 6.7.2
        McMurchie-Davidson scheme
      17. 6.7.3
        Dupuis-King-Rys scheme
      18. 6.7.4
        Pople-Hehre calculation of ERIs
      19. 6.7.5
        The PRISM algorithm
      20. 6.8
        The Resolution of the identity (RI) method
      21. 6.9
        Storage of ERIs
    13. Solution of the Self-Consistent Field (SCF) problem
    14. Conventional Roothaan-Hall SCF, the trial and error method, iterative solution of the Roothaan-Hall equations, initial guess, diagonalization of the core hamiltonian, extended Hückel type guess, INDO and MNDO guess, guess from atomic densities, basis set expansion, solution of the pseudo-eigenvalue problem, canonical orthonormalization, spectral form of S, Schmidt orthonormalization, symmetric orthonormalization, density matrices, projector idempotency constraint, Jacobi diagonalization, Givens-Householder diagonalization, stationary state conditions (with regard to orbitals and basis functions), unitary transformation of MOs, mixing of occupied and virtual orbitals, orbital rotation, energy gradient with regard to expansion coefficients, Brillouin theorem, construction of the Fock matrix, permutational symmetry of ERIs, supermatrix formalism, Raffenetti ordering, timings for construction of the F matrix.

      1. 7
        Solution of the SCF Problem
      2. 7.1
        Conventional Roothaan-Hall SCF
      3. 7.2
        Initial Guess
      4. 7.2.1
        Available methods for setting up the initial guess
      5. 7.2.2
        Improvement of starting orbitals - Basis set expansion
      6. 7.2.3
        Reuse of other wave-functions
      7. 7.3
        Solution of the pseudo-eigenvalue problem
      8. 7.4
        Orthogonalization procedures
      9. 7.4.1
        Schmidt procedure - successive orthonormalization
      10. 7.4.2
        Löwdin procedure
      11. 7.4.3
        Comparison of orthonormalization procedures
      12. 7.4.4
        Comparison between nonorthogonal and orthogonal basis set descriptions
      13. 7.5
        Diagonalization procedures
      14. 7.6
        Stationary state conditions for the SCF
      15. 7.7
        Construction of the Fock matrix
      16. 7.7.1
        Raffenetti ordering
    15. Convergence of SCF calculations
    16. Convergence criteria for SCF, convergence problems, oscillations, state switching, divergence, counteractions, convergence acceleration, state loyalty, univariate search methods, Fock matrix partitioning, pseudocanonical orbitals, l-dependent form of F, mixing coefficient, energy gradient with regard to l, Bessel equation, overlap of spinorbitals, Camp-King method, unitary transformation by an exponential matrix, diagonalization of a rectangular matrix, orbital rotation, extrapolation methods, Hartree damping, dynamic damping, 3-point extrapolation, Aitken d2 method, 4-point extrapolation, level shifting, starting and termination strategies, Pulay's DIIS, linear dependence of changes in F and P, errors in P and stationary state conditions, ADEM-DIOS, QC-SCF, linear convergence, quadratic convergence, orbital mixing expressed by a CI formalism, Newton-Raphson formulation of the SCF problem.

      1. 8.1
        General aspects: Convergence and convergence problems
      2. 8.1.1
        What to do in case of convergence problems?
      3. 8.2
        Univariate search methods and state loyalty
      4. 8.2.1
        Pople-Seeger method
      5. 8.2.2
        State loyalty by the Pople-Seeger method
      6. 8.2.3
        Camp-King method
      7. 8.2.4
        Implementation of the Camp-King method
      8. 8.3
        Extrapolation methods
      9. 8.3.1
        Damping
      10. 8.3.2
        Dynamic damping
      11. 8.3.3
        Aitken method
      12. 8.3.4
        Roothaan-Bagus-Sack method
      13. 8.4
        Level shifting
      14. 8.5
        Direct inversion of the iterative subspace (DIIS)
      15. 8.5.1
        Precursors of DIIS
      16. 8.5.2
        Practical aspects of DIIS
      17. 8.5.3
        Extension of DIIS: ADEM-DIOS
      18. 8.6
        Quadratically convergent SCF (QC-SCF)
      19. 8.6.1
        Linear and quadratic convergence
      20. 8.6.2
        QC-SCF method
      21. 8.6.3
        Comparison with normal SCF
      22. 8.6.4
        Implementation of QC-SCF in an ab initio program
      23. 8.7
        Overview of starting and terminating convergence methods
    17. SCF for open shell cases
    18. Different open shell cases, generalized Brillouin theorem, generalized HF equations, coupling terms, generalized Roothaan-Hall equations, partitioned HF (PHF); ROHF according to Roothaan; the McWeeny method for ROHF; unrestricted HF (UHF); Pople-Nesbet equations; properties of the UHF energy; dissociation problem by RHF and UHF; UHF wave function; the expectation value of S2; spin contamination; spin projection methods; UHF electron and spin densities.

      1. 9.1
        Derivation of a minimum condition for restricted open shell cases - generalized Brillouin theorem
      2. 9.2
        Generalized restricted open shell theory
      3. 9.2.1
        General derivation and relationship to MCSCF
      4. 9.2.2
        Derivation of the pseudo-eigenvalue equations
      5. 9.2.3
        LCAO Ansatz for ROHF - Generalized Roothaan-Hall equations
      6. 9.2.4
        Coupling coefficients aIJ and bIJ
      7. 9.3
        Partitioned HF (PHF)
      8. 9.4
        Roothaan's ROHF
      9. 9.5
        McWeeny' ROHF
      10. 9.6
        Unrestricted HF theory (UHF)
      11. 9.6.1
        Pople-Nesbet equations
      12. 9.6.2
        Properties of the UHF energy
      13. 9.6.3
        The dissociation problem
      14. 9.6.4
        The UHF wave-function
      15. 9.6.5
        Spin projection methods
      16. 9.6.5.1
        Spin constraint UHF (SUHF)
      17. 9.6.6
        UHF electron density and spin density distribution
      18. 9.6.7
        Calculation of hyperfine coupling constants
    19. General HF Theory
    20. Complex GHF, real GHF, complex UHF, real UHF, complex RHF, real RHF, form of general spinorbitals, possible constraints, internal and external stability, stability test, form of the Hessian, symmetry dilemma of UHF, singlet instability, non-singlet instabilities, complex HF, the O2 molecule and its 1Dg state, complex orbitals vs. real orbitals, complex Fock matrix, complex HF equations, eigenvalues for the complex problem, flow chart diagram.

      1. 10.1
        Constraints to complex GHF
      2. 10.2
        Stability tests
      3. 10.2.1
        Singlet instability
      4. 10.2.2
        Non-singlet instabilities
      5. 10.3
        Complex HF (CHF)
      6. 10.3.2
        Necessity of using complex HF - the O2 example
      7. 10.3.1
        Form of complex orbitals
      8. 10.3.2
        Roothaan Hall for CHF
    21. Direct SCF methods for large molecules
    22. M4-myth, number of ERIS for large molecules, storage problem, recalculation of ERIS; prescreening of two-electron integrals; batch processing, recurrence formula for the Fock matrix; cost for an ERI in dependence of l, selective storage of integrals; minimization of errors; changes in the number of ERIs per iteration step

      1. 11.1
        Number of ERIs for large molecules
      2. 11.2
        Flow chart for a DSCF program
      3. 11.3
        Prescreening of ERIs and neglecting of ERIs
      4. 11.4
        Recursion formula for the Fock matrix
      5. 11.5
        Selective storage of ERIs - Semi-direct SCF
      6. 11.6
        Error progression in a DSCF
      7. 11.7
        DSCF calculations for large molecules
  6. Ab Initio Methods II: Electron Correlation Methods (CI and Perturbation Theory)
    1. A. Electron Correlation

    2. Why do we need correlation corrected methods?
      1. 1.1
        Shortcomings of the HF approach
      2. 1.2
        What is correlation?
    3. Electron Density Functions: Density Matrices
      1. 2.1
        Reduced density matrices
      2. 2.2
        Energy in terms of Gp - N-representability problem
      3. 2.3
        Pair density distribution
      4. 2.4
        Fermi hole and Coulomb hole
      5. 2.5
        Density matrices in HF theory - Fock-Dirac density matrix
      6. 2.6
        Pictorial display of electron correlation
    4. Definition of the Correlation Energy
      1. 3.1
        Magnitude of the correlation energy
      2. 3.2
        Correlation energies from experimental data
    5. Types of Electron Correlation
      1. 4.1
        Static and dynamic electron correlation
      2. 4.2
        Electron Pair correlation
      3. 4.3
        Left-right, angular, in-out correlation
      4. 4.4
        Intraatomic and interatomic correlation
      5. 4.5
        Internal and external correlation
      6. 4.6
        Higher correlation effects and higher excitations
    6. What Correlation methods are available?

      B. Configuration Interaction

      CI wave function, properties of CI methods, full CI, truncated CI, tape driven and integral driven CI, UGA, SGA

    1. General Considerations
      1. 1.1
        How many terms are in the full CI wave function
      2. 1.2
        CI matrix
      3. 1.3
        Calculation of the CI correlation energy
    2. Full CI for H2
    3. Truncated CI: CID and CISD
    4. Conventional CI calculations
      1. 4.1
        Integral transformation
      2. 4.2
        Construction of spin-adapted CSF
      3. 4.3
        Calculation of matrix elements
      4. 4.4
        Diagonalization methods: Nesbet method, Davidson method
    5. Direct CI
      1. 5.1
        Multipurpose direct CISD
      2. 5.2
        A CISD program
    6. Correlation Orbitals - Natural Orbitals
      1. 6.1
        Correlation orbitals
      2. 6.2
        Natural orbitals
      3. 6.3
        Calculation of natural orbitals
      4. 6.4
        Natural orbitals of H2O
      5. 6.5
        Iterative natural orbital method
    7. Basis sets for correlation calculations
      1. 7.1
        Repetition of some basic terms
      2. 7.2
        Pople's basis sets
      3. 7.3
        Dunning's correlation consistent basis sets
      4. 7.4
        ANO basis sets
      5. 7.5
        Dual basis sets
    8. Error consistency
      1. 8.1
        Basis set error consistency: truncation error and BSSE
      2. 8.2
        BSSE (counterpoise method; inter- and intramolecular BSSE)
      3. 8.3
        Method error consistency: correlation error and size-extensivity error
      4. 8.4
        Size-extensivity - Size-extensivity versus size-consistency
      5. 8.5
        Size-extensivity error of CI
      6. 8.6
        Size-extensivity corrections: Davidson correction, Pople correction

      C. Many-Body Perturbation Theory

    1. Rayleigh-Schrödinger Perturbation Theory
      1. 1
        General perturbation theory formulas, intermediate normalization, E(0) representation, second order, third order, fourth order corrections
    2. Møller-Plesset Perturbation Theory
      1. 2.1
        First order correction to the energy Eorb
      2. 2.2
        Second order correction to the energys
      3. 2.3
        First order correction to the wave function
      4. 2.4
        Third order correction to the energy
      5. 2.5
        The original MP perturbation operator
    3. Epstein-Nesbet Perturbation Theory
      1. 3.1
        The EN perturbation operator
      2. 3.2
        Second order correction to the energy
      3. 3.3
        Advantages and disadvantages of EN perturbation theory
    4. Diagrammatic Perturbation Theory
      1. 4.1
        Introduction to diagrams
      2. 4.2
        Hugenholtz diagrams
      3. 4.3
        Goldstone diagrams rules, calculation of second order and third order energy
      4. 4.4
        Brandow diagrams
      5. 4.5
        How many diagrams exist at MBPTn?
    5. General Perturbation Theory
    6. Model space and orthogonal space, projection operators.

      1. 5.1
        Feshbach operator
      2. 5.2
        Brillouin-Wigner Perturbation Theory
      3. 5.3
        Resolvent expansion of energy and wave function
      4. 5.4
        General Rayleigh-Schrödinger Perturbation Theory
      5. 5.5
        Fourth order MP Theory (derivation of the energy formula)
      6. 5.6
        General MPn Theory (MP5, MP6, etc.)
    7. Dependence on the number of particles
      1. 6.1
        Investigation of first, second, and third order energy
      2. 6.2
        Size-extensivity of MP energies
      3. 6.3
        Linked diagram expansion first order wave operator and first order wave function second order wave operator and second order wave function combination of wave operator and perturbation operator diagrams derivation of the fourth order energy, factorization theorem.
      4. 6.4
        Linked Diagram Theorem
      5. 6.5
        Characterization of diagrams
    8. Convergence of the MPn series
      1. 7.1
        Convergence behavior (oscillations, divergence)
      2. 7.2
        Convergence radius and intruder states
      3. 7.3
        Convergence radius and intruder states
      4. 7.4
        Extrapolation procedures: Pade approximants
      5. 7.5
        Extrapolation formulas
      6. 7.6
        Extrapolation procedures: First order and higher order Feenberg scaling
    9. Projected MP Theory
      1. 8.1
        Annihilation versus projection methods
      2. 8.2
        Calculation of <S2> corrections
      3. 8.3
        PUHF, PMP2 and PMP3
      4. 8.4
        Practical considerations
    10. Application of MP Theory
      1. 9.1
        Cost considerations and feasibility
      2. 9.2
        Programming considerations
      3. 9.3
        Electron density analysis of MP response densities
      4. 9.4
        MP geometries
      5. 9.5
        MP energies
      6. 9.6
        MP dipole moments and other first order properties
      7. 9.7
        MP frequencies and IR intensitie
      8. 9.8
        Advantages and disadvantages of MP theory
    11. Greens Functions
      1. 10.1
        One-particle Green's functions
      2. 10.2
        One-particle Green's functions for an N-electron system
      3. 10.3
        Calculation of ionization potentials and electron affinities
      4. 10.4
        How to solve the Dyson equation?
      5. 10.5
        Relationship between the Green's function method and perturbation theory
      6. 10.6
        Application of Green's functions
  7. Ab initio Methods III: Electron Correlation Methods (From Single to Multi Configuration methods)
    1. Basic Concepts - A repetition
      1. 1.1
        Time-dependent Schrödinger Equation
      2. 1.2
        Born-Oppenheimer Approximation
      3. 1.3
        Variational Methods for ground and excited states
      4. 1.4
        Size consistence and size-extensiveness
    2. Single reference - multi determinant problems
      1. 2.1
        Reference, Configuration, and Determinant
      2. 2.2
        General ROHF
      3. 2.2.1
        Generalized Brillouin Theorem
      4. 2.2.2
        Generalized HF Equations
      5. 2.2.3
        Generalized Roothaan Hall Equations
      6. 2.3
        The Low-Spin Open Shell Problem
      7. 2.3.1
        ROSS
      8. 2.3.2
        ROHF-MP
      9. 2.4
        From ROHF to MCSCF
    3. Two-Configuration Descriptions
      1. 3.1
        GVB
    4. MCSCF
      1. 4.1
        Energy Expression in MCSCF
      2. 4.2
        CI Equations and Generalized Brillouin Theorem
      3. 4.3
        Methods to determine the MCSCF wave function
      4. 4.3.1
        Super CI Technique
      5. 4.3.2
        Quadratically Convergent MCSCF Methods: Newton Raphson Method
      6. 4.4
        The H2 molecule
    5. CASSCF
  8. Ab Initio Methods V: Calculation of Molecular Properties
    1. Overview over Molecular Properties
      1. 1.1
        Classification of Molecular Properties (1- and 2-electron properties; first order, second order and higher order properties; operational classifications; properties derived from the PES, from the wave-function; response properties; properties that involve more than one electronic state, properties that are beyond the Born-Oppenheimer approximation)
      2. 1.2
        Properties derived from the PES (energy derivatives: forces, harmonic, cubic, quartic force constants; infrared and Raman intensities; dipole moment, dipole polarizability, dipole hyperpolarizability, magnetic moment, magnetic susceptibility, magnetic hypersusceptibility; electrical anharmonicity; nuclear magnetic shieldings, NMR spin-spin coupling constants)
    2. Ab initio Energies
      1. 2.1
        From ab initio Energies to heats of formation
        1. 2.1.1
          Correction of heats of formation from T to 0 K
        2. 2.1.2
          Calculation of experimental molecular energies
        3. 2.1.3
          Calculation of theoretical energies within the Born-Oppenheimer approximation
        4. 2.1.4
          Estimation of relativistic effects
        5. 2.1.5
          Estimation of correlation energies
        6. 2.1.6
          How to get to HF limit energies
      2. 2.2
        Practical considerations
      3. 2.3
        Direct Calculation of Thermodynamic Properties (partition functions; translational, rotational, vibrational corrections; calculation of ZPE and entropy;calculation of enthalpy and free enthalpy; how to read the thermochemistry output of an ab initio program)
      4. 2.4
        Heats of formation from ab initio Energies: The G Theoretical Model Chemistry
        1. 2.4.1
          Basis set additivity
        2. 2.4.2
          Use of isogyric reactions
        3. 2.4.3
          Gaussian1 (G1) Theory
        4. 2.4.4
          G2 Theory
        5. 2.4.5
          Modifications: G2(MP2) and G2M
        6. 2.4.6
          G3 Theory
      5. 2.5
        Other ways of calculating heats of formation
        1. 2.5.1
          Dewar's approach
        2. 2.5.2
          Bond Additivity Corrections (BAC) method
        3. 2.5.3
          Transition metal chemistry: PCI80
      6. 2.6
        The CBS Theoretical Model Chemistry
        1. 2.6.1
          Determination of the SCF limit
        2. 2.6.2
          Determination of PNOs
        3. 2.6.3
          CBS Pair energies
        4. 2.6.4
          CBS-QCI/APNO model
      7. 2.7
        Heats of Formation from Formal Reactions
        1. 2.7.1
          Bond separation energies and isodesmic reactions
        2. 2.7.2
          Homodesmotic reactions and super-homodesmotic reactions
        3. 2.7.3
          Resonance and strain energies from homodesmotic reactions
    3. Interpretation of the wave function
      1. 3.1
        Properties of the molecular wave function
        1. 3.1.1
          The Hellmann-Feynman theorem
        2. 3.1.2
          The virial theorem
        3. 3.1.3
          Methods with and without a wave function
      2. 3.2
        Orbital energies
        1. 3.2.1
          Koopmans theorem
        2. 3.2.2
          When does Koopmans theorem apply?
        3. 3.2.3
          Excitation energies from orbital energies (Singlet and triplet states)
        4. 3.2.4
          Orbital energies and total energy
      3. 3.3
        Population analysis
        1. 3.3.1
          Mulliken population analysis
        2. 3.3.2
          Shortcomings of the Mullkien population analysis
        3. 3.3.3
          Improvements of the Mulliken population analysis
        4. 3.3.4
          Modified atomic orbitals (MAOs)
        5. 3.3.5
          Charges from the electrostatic potential
        6. 3.3.6
          Weinhold's natural population analysis: NAOs and NBOs
      4. 3.4
        The shape of canonical Molecular Orbitals
        1. 3.4.1
          How to read the coefficients of MOs?
        2. 3.4.2
          Delocalized and localized MOs
        3. 3.4.3
          Graphical representations of MOs
      5. 3.5
        Localization of MOs
        1. 3.5.1
          Localization criteria
        2. 3.5.2
          Boys localization
        3. 3.5.3
          Edminston-Ruedenberg localization
        4. 3.5.4
          Magnasco-Perico localization
        5. 3.5.5
          Pipek-Mezey localization
    4. Analysis of the electron density distribution
      1. 4.1
        Properties of the electron density distribution
      2. 4.2
        Difference density distribution
      3. 4.3
        Measurement of the electron density distribution
      4. 4.4
        Ways of analyzing the electron density distribution
      5. 4.5
        Topological analysis
      6. 4.6
        Theory of virial subspaces
        1. 4.6.1
          Open and closed systems
        2. 4.6.2
          Zero-flux surfaces
        3. 4.6.3
          Bader's atoms in molecules theory
        4. 4.6.4
          Atomic properties
      7. 4.7
        The Laplacian of the electron density distribution
        1. 4.7.1
          The local virial theorem
        2. 4.7.2
          Bond and lone pair concentrations
        3. 4.7.3
          The shell structure of the atoms
      8. 4.8
        Description of the chemical bond
        1. 4.8.1
          The electrostatic description of the chemical bond
        2. 4.8.2
          Ruedenberg's description of the chemical bond
        3. 4.8.3
          Bader's description of the chemical bond
        4. 4.8.4
          Bond order, bond ellipcity, and bond polarity
        5. 4.8.5
          A general model of covalent bonds (Cremer-Kraka criteria)
        6. 4.8.6
          Bond energies and bond dissociation energies
        7. 4.8.7
          Bond strength as related to intrinsic properties of the bond
        8. 4.8.8
          Overlap and electronegativity
    5. Molecular properties from analytical energy derivatives
      1. 5.1
        Analytical derivatives in HF theory
        1. 5.1.1
          HF first derivatives
        2. 5.1.2
          HF second derivatives
        3. 5.1.3
          Coupled Perturbed Hartee-Focck (CPHF) theory
        4. 5.1.4
          Implementation according to Pople
        5. 5.1.5
          The z-vector formalism of Handy and Schaefer
        6. 5.1.6
          Overview over RHF and GROHF derivatives
      2. 5.2
        MPn derivatives
      3. 5.3
        MCSCF and CASSCF derivatives
      4. 5.4
        CI derivatives
      5. 5.5
        Implementation of derivatives in an ab initio program
      6. 5.6
        General response theory
        1. 5.6.1
          Expectation value versus response property
    6. Molecular Geometries and Geometry Optimizations
      1. 6.1
        Basic definitions and overview
      2. 6.2
        Optimization methods - Coordinate systems
        1. 6.2.1
          Coordinates used for optimization (redundant, nonredundant)
        2. 6.2.2
          Relationship between internal and Cartesian coordinates: B matrix
        3. 6.2.3
          Relationships for redundant coordinates: G and K matrices
        4. 6.2.4
          Gradient and forces for non-redundant and redundant coordinates
        5. 6.2.5
          Optimization in redundant internal coordinates
        6. 6.2.6
          Conversion from redundant internal to Cartesian coordinates
        7. 6.2.7
          Advantages of redundant coordinates
        8. 6.2.8
          Natural internal coordinates of Pulaty and Boggs
        9. 6.2.9
          Delocalized internal coordinates of Baker
        10. 6.2.10
          Use of Cartesian coordinates in optimizations
      3. 6.3
        Optimization methods - general features
        1. 6.3.1
          Use of the Hessian for optimizations
        2. 6.3.2
          Convergence criteria
        3. 6.3.3
          Stepsize and search direction
        4. 6.3.4
          Search for a local minimum
        5. 6.3.5
          Search for a transition state
      4. 6.4
        Optimization methods - general features
        1. 6.4.1
          Non-derivative methods (Univariate search, Simplex method)
        2. 6.4.2
          Gradient methods (Steepesct descent, Conjugate gradient methods)
        3. 6.4.3
          Quasi-Newton methods (Davidon-Fletcher-Powell, Murtagh-Sargent)
        4. 6.4.4
          Newton-Raphson methods
      5. 6.5
        Special search techniques
        1. 6.5.1
          Minimum search - Schlegel's method
        2. 6.5.2
          Transition state searches
        3. 6.5.3
          Mode following method of Baker
        4. 6.5.4
          Up-hill searches
        5. 6.5.5
          Rational functional methods
      6. 6.6
        Definition of the molecular geometry
        1. 6.6.1
          What is the difference between re, rg, ra, r0, rv, rz?
        2. 6.6.2
          Quality of HF geometries
        3. 6.6.3
          MP and CC geometries
        4. 6.6.4
          DFT geometries
    7. Conformational processes
      1. 7.1
        Basic terms: Conformations and conformers
      2. 7.2
        Internal rotation
        1. 7.2.1
          Rigid and flexible rotors
        2. 7.2.2
          Fourier expansion of the rotational potential
        3. 7.2.3
          Rotational barriers and their electronic nature
        4. 7.2.4
          Coupled rotors: Fourier expansion and chemical relevance
      3. 7.3
        Inversion of molecular conformations
        1. 7.3.1
          Inversion barriers and electronic nature
      4. 7.4
        Ring puckering and pseudorotation
        1. 7.4.1
          The ring puckering coordinates: ring inversion and ring pseudorotation
        2. 7.4.2
          Conformational space: Dimension and basis conformations
        3. 7.4.3
          The cyclohexane globe and its extensions
        4. 7.4.4
          Relationship between acyclic rotors and cyclic pseudorotors
      5. 7.5
        Acyclic pseudorotors
        1. 7.5.1
          Berry pseudorotation
      6. 7.6
        Bond pseudorotation
    8. Vibrational frequencies and force constants
      1. 8.1
        Basic terms: Conformations and conformers
        1. 8.1.1
          The vibrational energy levels in the harmonic approximation
        2. 8.1.2
          Anharmonic vibration and More potential
        3. 8.1.3
          Vibrational selection rules
        4. 8.1.4
          Vibration-rotation spectrum
        5. 8.1.5
          Raman vibrational spectrum
      2. 8.2
        Classical calculation of the normal modes of a polyatomic molecule
        1. 8.2.1
          Cartesian vs. internal coordinates: Wilson B matrix
        2. 8.2.2
          Mass-weighted coordinates and Wilson G matrix
        3. 8.2.3
          The harmonic approximation
        4. 8.2.4
          Derivation of the Euler-Lagrange equations
        5. 8.2.5
          Generalized force constants and force constant matrix
        6. 8.2.6
          Calculation of normal modes in terms of Cartesian and internal coordinates
      3. 8.3
        Infrared and Raman spectra
        1. 8.3.1
          Vibrational selection rules
        2. 8.3.2
          Theory of infrared intensities (harmonic approximation)
        3. 8.3.3
          Calculation of IR intensities with HF and correlated methods
        4. 8.3.4
          Absolute and relative IR intensities, intensities of isotopomers
        5. 8.3.5
          Calculation of the Raman spectrum
      4. 8.4
        Determination of local modes
        1. 8.4.1
          Isolated stretching modes
        2. 8.4.2
          Local modes from overtone spectroscopy
        3. 8.4.3
          Adiabatic internal modes (AIMs)
        4. 8.4.4
          The properties of AIMs
      5. 8.5
        Analysis of vibrational spectra
        1. 8.5.1
          Normal mode analysis
        2. 8.5.2
          Potential energy analysis
        3. 8.5.3
          Characterization of normal modes in terms of AIMs
        4. 8.5.4
          Spectra of isotopomers and their calculation
        5. 8.5.5
          Correlation of vibrational spectra
        6. 8.5.6
          Charges from vibrational intensities
      6. 8.6
        Vibrational-rotational coupling
        1. 8.6.1
          Coriolis forces
      7. 8.7
        The effects of anharmonicity
        1. 8.7.1
          Overtones and combination bands
        2. 8.7.2
          Fermi resonances
        3. 8.7.3
          Calculation of cubic and quartic force constants
        4. 8.7.4
          Vibrational corrections of measured geometries
      8. 8.8
        The role of force constants for describing bond strength
        1. 8.8.1
          Badger rule
        2. 8.8.2
          Force constants from experimental spectra
        3. 8.8.3
          Force constants and the intrinsic bond dissociation energy
    9. Ionization potentials
      1. 9.1
        Koopmans theorem and its applicability
      2. 9.2
        PE and ESCA spectroscopy
      3. 9.3
        Explicit calculation of ionization potentals
      4. 9.4
        Ionization potentials from Green function methods
    10. Electric properties
      1. 10.1
        The response to electric fields
        1. 10.1.1
          Molecular response parameters
        2. 10.1.2
          General theory of response properties in an external electric field
        3. 10.1.3
          One- and two-electron properties
      2. 10.2
        Electric multipole moments
        1. 10.2.1
          Dipole moments
        2. 10.2.2
          Quadrupole moments
        3. 10.2.3
          Higher moments
        4. 10.2.4
          Use of multipole moments: Distributed multipole expansion
      3. 10.3
        Electric field gradient and nuclear quadrupole coupling constant
      4. 10.4
        Electrostatic potential
      5. 10.5
        The molecular polarizability
        1. 10.5.1
          The static electric polarizability
        2. 10.5.2
          Polarizability and molecular properties
        3. 10.5.3
          Hyperpolarizabilities
      6. 10.6
        Bulk electrical properties
        1. 10.6.1
          The relative permittivity and the electric susceptibility
        2. 10.6.2
          Polar molecules
        3. 10.6.3
          Refractive index and dynamic polarizability
      7. 10.7
        Optical activity
        1. 10.7.1
          Circular birefringence and optical rotation
        2. 10.7.2
          Magnetically induced polarization
        3. 10.7.3
          Rotational strength
    11. Magnetic properties
      1. 11.1
        Interactions of magnetic fields with molecules: response properties
      2. 11.2
        Diamagnetism and paramagnetism
        1. 11.2.1
          Diamagnetism
        2. 11.2.2
          Magnetic dipole moment, magnetizability, and magnetic susceptibility
        3. 11.2.3
          Paramagnetism
      3. 11.3
        Vector functions and their derivatives - a repetition
        1. 11.3.1
          Derivatives of vector functions
        2. 11.3.2
          The vector potential
      4. 11.4
        Description of magnetic properties by perturbation theory
        1. 11.4.1
          The perturbed Hamiltonian
        2. 11.4.2
          Calculation of diamagnetic and paramagnetic susceptibility
        3. 11.4.3
          Diamagnetic and paramagnetic current density
      5. 11.5
        Calculation of NMR chemical shifts
        1. 11.5.1
          Shielding constants
        2. 11.5.2
          Diamagnetic contribution to shielding
        3. 11.5.3
          Paramagnetic contribution to shielding
        4. 11.5.4
          The GIAO method
        5. 11.5.5
          The IGLO method
        6. 11.5.6
          The LORG method
        7. 11.5.7
          GIAO-MP and other methods
        8. 11.5.8
          The IGLO-DFT method
        9. 11.5.9
          Results of NMR chemical shift calculations
        10. 11.5.10
          Choice of the reference
        11. 11.5.11
          The NMR-ab initio-IGLO method
        12. 11.5.12
          IGLO-PISA method
        13. 11.5.13
          State-of-the-art theory: Relativistic corrections
      6. 11.6
        Spin-spin coupling in ESR (Electron Spin Resonance)
        1. 11.6.1
          Hamiltonian for electron spin coupling
        2. 11.6.2
          Hyperfine splitting constants
        3. 11.6.3
          Calculation of the Fermic contact term
        4. 11.6.4
          Results of unrestricted versus restricted theory
        5. 11.6.5
          Interpretation of ESR spectra
      7. 11.7
        NMR spin-spin coupling constants
        1. 11.7.1
          Mechanism of spin-spin coupling between nuclei
        2. 11.7.2
          The spin-spin coupling Hamiltonian
        3. 11.7.3
          Ab initio methods for calculating NMR coupling constants
        4. 11.7.4
          DFT methods for calculating NMR coupling constants
        5. 11.7.5
          Results obtained with the EOM-CC method
        6. 11.7.6
          Karplus curves and determination of molecular conformations
        7. 11.7.7
          Longe range coupling constants
        8. 11.7.8
          Relationships between coupling constants and other molecular quantities
    12. Excited states of molecules
      1. 12.1
        Excited states of a diatomic molecule - a repetition
        1. 12.1.1
          Coupling of angular momentum: Hund coupling
        2. 12.1.2
          Selection rules
        3. 12.1.3
          Vibronic transitions: Franck-Condon principle
      2. 12.2
        Electronic spectra of polyatomic molecules
        1. 12.2.1
          Chromophores
        2. 12.2.2
          Vibronically allowed transitions
        3. 12.2.3
          Singlet-triplet transitions
        4. 12.2.4
          Non-radiative decay
        5. 12.2.5
          Radiative decay: Fluorescence and phosphorescence
        6. 12.2.6
          Intersystem crossing
      3. 12.3
        Ab initio methods for calculating excited states
        1. 12.3.1
          General problems of calculating excited states
        2. 12.3.2
          The CIS method and its extensions
        3. 12.3.3
          CASSCF and CAS-PT2
        4. 12.3.4
          EOM-CC methods
        5. 12.3.5
          DFT for excited states
    13. Molecular interactions and molecular solvation
      1. 13.1
        Weak molecular interactions: van der Waals complexes
      2. 13.2
        Forces acting in van der Waals complexes
        1. 13.2.1
          Electrostatic interactions between molecules
        2. 13.2.2
          Induced electrostatic interactions
        3. 13.2.3
          Polarizability and dispersion forces
        4. 13.2.4
          Overlap or exchange repulsion
      3. 13.3
        Binding energies and geometries of van der Waals complexes
        1. 13.3.1
          Basis set and method requirements
        2. 13.3.2
          Basis set superposition error and counterpoise method
        3. 13.3.3
          Failure of DFT
        4. 13.3.4
          Typical binding energies and geometries
      4. 13.4
        Perturbation theory for intermolecular forces
        1. 13.4.1
          Short-range perturbation theory
        2. 13.4.2
          Symmetry-adapted perturbation theories
        3. 13.4.3
          First order and second order terms
      5. 13.5
        Electron density description of van der Waals complexes
        1. 13.5.1
          Difference densities and Laplace concentrations
      6. 13.6
        Solvation of soluted molecules
        1. 13.6.1
          Difference between gas phase and solution properties
        2. 13.6.2
          The supermolecule approach
        3. 13.6.3
          Continuum models for describing solvation
        4. 13.6.4
          Cavitation models
        5. 13.6.7
          Monte Carlo calculations
        6. 13.6.8
          Methods of molecular dynamics
      7. 13.7
        Practical Models for intermolecular potentials
  9. Density Functional Theory
    1. Introduction to DFT
      1. 1.1
        History of DFT (Thomas-Fermi model)
      2. 1.2
        Present and future impact of DFT on Chemistry
    2. Properties of the exact electron density distribution
      1. 2.1
        Why to use a density-based theory?
    3. Hohenberg-Kohn Theorems
      1. 3.1
        Searching for the ground-state energy
      2. 3.2
        The first Hohenberg-Kohn Theorem
      3. 3.3
        The second Hohenberg-Kohn Theorem
      4. 3.4
        Spin Polarization
      5. 3.5
        Scheme for calculations based on the Hohenberg-Kohn theorems
    4. Kohn-Sham Equations
      1. 4.1
        Partitioning of the Hohenberg-Kohn functional F[n]
      2. 4.2
        The decomposition of the kinetic energy T[n]
      3. 4.3
        The decomposition of the potential energy V[n]
      4. 4.4
        The Kohn-Sham equations
      5. 4.5
        The adiabatic connection scheme
      6. 4.6
        Partitioning into exchange and correlation contributions
    5. Uniform Electron Gas: The Local Density Approximation (LDA)
      1. 5.1
        The main idea
      2. 5.2
        Exchange in LDA
      3. 5.3
        Correlation in LDA
      4. 5.4
        Advantages and disadvantages of LDA
    6. Gradient Corrected DFT
      1. 6.1
        Gradient expansion
      2. 6.2
        Generalized Gradient Approximation (GGA)
      3. 6.3
        Exchange in GGA
      4. 6.4
        Correlation in GGA
    7. Overview over Density Functionals
      1. 7.1
        Exchange Functionals (Slater exchange, Xa approximation, Becke exchange correction, Becke-Roussel)
      2. 7.2
        Correlation Functionals (VWN, Perdew-Wang, Lee-Yang-Parr)
      3. 7.3
        Hybrid methods
    8. Improvement of Density Functionals
      1. 8.1
        Asymptotic behavior
      2. 8.2
        Limiting cases: homogenous systems, one-electron systems
      3. 8.3
        The Becke 95 correlation functional
      4. 8.4
        Exact KS potentials and their application
      5. 8.5
        Model KS potentials
    9. Implementation of DFT
      1. 9.1
        Programming of the Kohn-Sham Equations
      2. 9.2
        Numerical Quadrature (Gauss quadrature schemes, accuracy)
      3. 9.3
        Use of auxiliary bases for densities and potentials
      4. 9.4
        Available DFT programs
      5. 9.5
        DFT in Gaussian94
    10. DFT methods with Linear scaling
      1. 10.1
        Fast multipole method
      2. 10.2
        KWIK
      3. 10.3
        Integration of functionals using PYS balls
      4. 10.4
        Use of plane waves
      5. 10.5
        Use of wavelets
    11. Application of DFT methods
      1. 11.1
        Basis sets for DFT
      2. 11.2
        Energy derivatives
      3. 11.3
        Energies and geometries
      4. 11.4
        Vibrational frequencies and IR intensities
    12. Calculation of magnetic properties with DFT methods
      1. 12.1
        Uncoupled DFT methods
      2. 12.2
        SOS-DFPT methods
      3. 12.3
        Current-DFT - An unsolved problem
    13. DFT and Excited States
      1. 13.1
        Hohenberg-Kohn theorems and excited states
      2. 13.2
        Approaches to treat excited states
      3. 13.3
        ROSS-DFT and MCSCF-DFT
    14. Transition states and van der Waals complexes
      1. 14.1
        Basic Failures when describing transition states
      2. 14.2
        Description of H bonding
      3. 14.3
        Description of van der Waals complexes
      4. 14.4
        Improvement of DFT
    15. DFT and Chemical Concepts
      1. 15.1
        Chemical potential and electronegativity
      2. 15.2
        Hardness and softness: HSAB concept
      3. 15.3
        Fukui function
  10. Mathematics for Quantum Chemists
    1. Vector algebra
      1. 1.1
        Scalar product
      2. 1.2
        Vector product
      3. 1.3
        Triple product
    2. Infinite series
      1. 2.1
        Fundamental concepts
      2. 2.1.1
        Geometrical series
      3. 2.1.2
        Harmonic series
      4. 2.1.3
        Alternating series
      5. 2.2
        Convergence criteria
      6. 2.2.1
        Cauchy criterion
      7. 2.2.2
        d'Almbert criterion
      8. 2.3
        Series expansion of functions
      9. 2.3.1
        Taylor series (MacLaurin’s series)
      10. 2.3.2
        Power series
      11. 2.4
        Complex numbers
      12. 2.4.1
        Elementary operations
      13. 2.4.2
        Euler representation
    3. Vector analysis
      1. 3.1
        Scalar and vector fields
      2. 3.2
        Vector calculus
      3. 3.2.1
        Curves
      4. 3.2.2
        Arclength
      5. 3.2.3
        Tangent, curvature and torsion
      6. 3.3
        Gradient, Ñ
      7. 3.4
        Divergence, Ñ•
      8. 3.5
        Curl, Ñx
      9. 3.6
        Successive application of Ñ operator, the Laplacian
      10. 3.7
        Integral relations (Gauss, Stokes)
    4. Coordinate systems
      1. 4.1
        Curvilinear coordinates
      2. 4.1.1
        Metric
      3. 4.1.2
        Gradient
      4. 4.1.3
        Divergence
      5. 4.1.4
        Laplacian
      6. 4.1.5
        Curl
      7. 4.2
        Rectangular Cartesian coordinates
      8. 4.3
        Circular cylindrical coordinates
      9. 4.4
        Spherical polar coordinates
    5. Tensors
      1. 5.1
        Linear mapping of vectors, second-rank tensors
      2. 5.2
        Basis, tensor coordinates and components
      3. 5.3
        Tensors of arbitrary rank
      4. 5.4
        Elementary operations with tensors
      5. 5.5
        Special tensor
      6. 5.6
        Principal axes and values
      7. 5.7
        Vector and tensor fields, tensor analysis
      8. 5.8
        Multipole moments, irreducible tensors
      9. 5.9
        Behavior of tensors under coordinate rotations
    6. Ordinary Differential Equations (ODE’s)
      1. 6.1
        General
      2. 6.2
        Order of ODE’s, explicit and implicit ODE’s
      3. 6.3
        Initial problems, several kinds of problems
      4. 6.4
        ODE’s of first order
      5. 6.4.1
        Some types of exactly solvable ODE’s
      6. 6.4.2
        Linear first-order ODE’s
      7. 6.4.3
        Existence and uniqueness of solutions, the initial-value problem for the 1st-order ODE
      8. 6.5
        ODE’s of higher order, systems of ODE’s
      9. 6.5.1
        Linear ODE of order ≥ 2
      10. 6.5.2
        Linear ODE of second order with constant coefficients
      11. 6.5.3
        Systems of linear ODE of second order with constant coefficients
      12. 6.5.4
        Initial value, boundary value, and eigenvalue problems
      13. 6.5.5
        Sturm-Liouville theory and special function systems
      14. 6.5.5.1
        Sturm-Liouville problems
      15. 6.5.5.2
        Some important systems of special functions
    7. Partial differential equations (PDE’s)
      1. 7.1
        Linear PDE of second order (LPDE2)
      2. 7.1.1
        The hyperbolic differential equation
      3. 7.1.2
        The parabolic differential equation
      4. 7.1.3
        The elliptic differential equation
      5. 7.2
        Some remarks on non-linear PDE’s
      6. 7.3
        Appendix A1: Spherical harmonics
      7. 7.4
        Appendix A2: Dirac’s d -function
    8. Variational calculus
      1. 8.1
        Functionals and functional derivatives
      2. 8.2
        Variational problems without constraints
      3. 8.3
        Variational problem with constraints
      4. 8.4
        Variational problems with local constraints
      5. 8.5
        Addendum: Ritz method for the Schrödinger equation
    9. Vector Spaces
      1. 9.1
        Vector Algebra: A short repetition
      2. 9.2
        Vector space
      3. 9.2.1
        Cartesian vector space R3
      4. 9.2.2
        Covariant and contravariant components of a vector
      5. 9.3
        Linear vector space
      6. 9.3.1
        Definition of linear space L
      7. 9.3.2
        Linear dependence and linear independence
      8. 9.4
        Unitary vector space
      9. 9.4.1
        Function space
      10. 9.5
        Norm of an element
      11. 9.6
        Cauchy-Schwarz Inequality
      12. 9.7
        Triangle Inequality
      13. 9.8
        Angle between two elements
      14. 9.9
        Distance between two elements
      15. 9.10
        Hilbert Space
      16. 9.10.1
        Cauchy Criterion
      17. 9.10.2
        Hilbert Space of the square-integrable functions
      18. 9.11
        Overview over Spaces
    10. Operators in Quantum Mechanics (DC)
      1. 10.1
        Linear Operators
      2. 10.2
        Eigenfunctions of linear operators
      3. 10.3
        Matrix elements
      4. 10.4
        Adjoint operators (Hermitian conjugate)
      5. 10.5
        Hermitian operators
      6. 10.5.1
        Properties of Hermitian Operators
      7. 10.5.2
        Examples of Hermitian operators
      8. 10.6
        Unitary operators and unitary transformations
      9. 10.6.1
        Unitary transformation
      10. 10.6.2
        Unitary transformation of an Hermitian operator
      11. 10.6.3
        The infinitesimal unitary operator
      12. 10.7
        Normal operators
      13. 10.8
        Projection operators
      14. 10.9
        Functions of operators
      15. 10.9.1
        Differentiation of an operator
      16. 10.10
        Commutator of operators
      17. 10.11
        Overview over operators used in Quantum Mechanics
    11. Matrices and Determinants
      1. 11.1
        Linear equation systems
      2. 11.2
        Some basic definitions
      3. 11.3
        Matrix addition and matirx multiplication
      4. 11.3.1
        Addition
      5. 11.3.2
        Multiplication
      6. 11.3.3
        Falk diagrams
      7. 11.3.4
        Commutating matrices
      8. 11.4
        Special matrices with real numbers
      9. 11.4.1
        Transposed Matrix
      10. 11.4.2
        Symmetric and anti(skew)-symmetric matrices
      11. 11.4.3
        Triangular matrix
      12. 11.5
        Determinants
      13. 11.6
        Rank of a matrix and singular matrix
      14. 11.7
        The inverse of a matrix
      15. 11.8
        Special matrices with complex numbers
      16. 11.8.1
        Complex and conjugate-complex matrices
      17. 11.8.2
        The adjoint (hermitian conjugate) matrix
      18. 11.8.3
        Hermitian and anti(skew)-Hermitian matrix
      19. 11.8.4
        Orthogonal and unitary matrices
      20. 11.8.5
        Normal matrices
      21. 11.9
        Overview over matrices
    12. Eigenvalue problems
      1. 12.1
        Solving linear equation systems
      2. 12.1.1
        Gauss elimination
      3. 12.1.2
        Existence and general properties of solutions
      4. 12.2
        Eigenvalue equations
      5. 12.3
        Eigenvalues of Hermitian and other matrices
      6. 12.3.1
        Similarity transformations and Invariants
      7. 12.3.2
        Invariants of an unitary transformation
      8. 12.3.3
        Estimates of the eigenvalues of Hermitian matrices
      9. 12.3.4
        The Raleigh quotient
      10. 12.4
        Eigenvalues of a complex matrix
      11. 12.5
        Diagonalization of matrices
      12. 12.5.1
        Jacobi diagonalization
      13. 12.5.1.1
        Algorithm for a Jacobi diagonalization
      14. 12.5.2
        Givens-Householder diagonalization
      15. 12.5.2.1
        Givens diagonalization
      16. 12.5.2.2
        Householder diagonalization
      17. 12.5.3
        Diagonalization of large matrices
      18. 12.5.4
        Lanczos method
      19. 12.5.5
        Nesbet method (see CI course)
      20. 12.5.6
        Davidson method (see CI course)
      21. 12.6
        Quadratic forms
      22. 12.6.1
        Differentiation of a quadratic form
      23. 12.6.2
        Definiteness of matrices
      24. 12.6.3
        Characterization of rectangular matrices
      25. 12.6.4
        Diagonalization of rectangular matrices
      26. 12.7
        Matrix Factorization
      27. 12.7.1
        LU Factorization and the Gaussian Elimination revisited
      28. 12.7.2
        The LDLT and Cholesky factorizations
      29. 12.7.3
        QR and QL (LQ) factorizations
      30. 12.7.4
        Spectral decomposition of a matrix
      31. 12.8
        A non-unit metric: Orthogonalization procedures
      32. 12.8.1
        Gram-Schmidt Orthonormalization
      33. 12.8.2
        Löwdin procedures
      34. 12.8.2.1
        Symmetric orthonormalization
      35. 12.8.2.2
        Canonical orthonormalization
      36. 12.8.3
        Comparison and application of orthonormalization procedures
      37. 12.9
        Overview over eigenvalue problems
    13. Optimization
      1. 13.1
        Definition of optimization problems
      2. 13.2
        Elements of multivariate analysis
      3. 13.2.1
        Continuity
      4. 13.2.2
        Differentiability, gradient, hessian
      5. 13.2.3
        Taylor’s theorem
      6. 13.2.3.1
        Finite difference approximations to derivatives
      7. 13.2.4
        Contour plots
      8. 13.3
        Stationary points of multivariate functions
      9. 13.3.1
        Minima, global and local
      10. 13.3.2
        Local versus global methods
      11. 13.3.3
        Convergence characterization
      12. 13.4
        Optimization methods used in Quantum Chemistry
      13. 13.4.1
        Energy-only methods
      14. 13.4.1.1
        Univariate search
      15. 13.4.1.2
        Simplex method
      16. 13.4.2
        Gradient methods
      17. 13.4.2.1
        Steepest descent methods
      18. 13.4.2.2
        Conjugate gradient methods
      19. 13.4.2.3
        Nonlinear conjugate gradient methods
      20. 13.4.3
        Newton methods
      21. 13.4.3.1
        Discrete Newton
      22. 13.4.3.2
        Quasi Newton methods
      23. 13.4.3.3
        Rank 1 methods, (Broyden’s method)
      24. 13.4.3.4
        Rank 2 methods
    14. Probability and Statistics
      1. 14.1
        Probability, definitions and theorems, Venn diagrams
      2. 14.1.1
        Counting sample points
      3. 14.1.2
        Probability of an event
      4. 14.1.2.1
        Additive rules
      5. 14.1.2.2
        Multiplicative rules
      6. 14.1.2.3
        Bayes’ rule
      7. 14.2
        Random variables and probability distributions
      8. 14.2.1
        Discrete probability distributions
      9. 14.2.2
        Continuous probability distributions
      10. 14.2.3
        Empirical distributions
      11. 14.2.3.1
        Stem and leaf plot
      12. 14.2.3.2
        Frequency distribution
      13. 14.2.4
        Joint probability distributions
      14. 14.2.4.1
        Marginal distributions
      15. 14.2.4.2
        Conditional probability distributions
      16. 14.2.4.3
        Statistical independence
      17. 14.3
        Mathematical expectation
      18. 14.3.1
        Mean of a random variable
      19. 14.3.2
        Variance and covariance, standard derivation
      20. 14.3.3
        Correlation coefficient
      21. 14.3.4
        Chebyshev’s theorm
      22. 14.4
        Some discrete probability distributions
      23. 14.4.1
        Discrete uniform distribution
      24. 14.4.2
        Binomial and multinomial distributions
      25. 14.4.2.1
        The Bernulli Process
      26. 14.4.3
        Hypergeometric distribution
      27. 14.4.4
        Poisson distribution and the Poisson process
      28. 14.5
        Some continuous probability distributions
      29. 14.5.1
        Continuous uniform distribution
      30. 14.5.2
        Normal distribution
      31. 14.5.3
        Areas under the normal curve
      32. 14.5.4
        Normal approximation to the binomial
      33. 14.5.5
        Gamma and exponential distributions
      34. 14.5.6
        Relationship between Gamma, exponential and Poisson distribution
      35. 14.5.7
        Other continuous distributions
      36. 14.5.7.1
        Chi-square distribution
      37. 14.5.7.2
        Logonormal distribution
      38. 14.5.7.3
        Weibull distribution
      39. 14.6
        Fundamental sampling distributions
      40. 14.6.1
        Central tendency in the sample
      41. 14.6.2
        Variability in the sample
      42. 14.6.3
        T-distribution
      43. 14.6.4
        F-distribution
    15. Catastrophe Theory
      1. 15.1
        The cusp catastrophe
      2. 15.2
        The dynamic that causes catastrophes
      3. 15.3
        The mechanism of aggression
      4. 15.4
        Divergence
      5. 15.5
        Thom’s classification theorem
      6. 15.6
        Thom’s seven elementary catastrophes
      7. 15.7
        The butterfly catastrophe
      8. 15.8
        Structural changes and molecular graphs
      9. 15.9
        Description of reaction mechanism: H2 + O(3P)
  11. Presentation Techniques in Chemistry – How to write a paper? How to give a seminar?
    1. Scientific Research and Scientific Writing
      1. 1.1
        The ultimate result of scientific research is publication
      2. 1.2
        Scientific communication is a 2-way process
      3. 1.3
        Thinking and Writing
      4. 1.4
        There is a well-defined path from thinking to writing
      5. 1.5
        From thinking to writing in TC
      6. 1.6
        List of questions to be answered before writing
    2. What is a “Scientific Paper”
      1. 2.1
        Types of scientific communications
      2. 2.2
        Definition of a scientific paper: primary publication
      3. 2.3
        Organization of a scientific paper
      4. 2.4
        Drafting a scientific paper
      5. 2.4.1
        The writing process
      6. 2.4.2
        Transitions
      7. 2.4.3
        The Role of tangible details
      8. 2.4.4
        Keeping the speed of writing.
      9. 2.5
        Perception of a paper
      10. 2.6
        Order of writing up the paper
      11. 2.7
        Preparing the actual write-up: Notes for authors
    3. The various parts of a Journal Article
      1. 3.1
        The Result part
      2. 3.2
        The Method part
      3. 3.3
        The Discussion part
      4. 3.4
        The Introduction part
      5. 3.5
        The Conclusion
      6. 3.6
        The Abstract
      7. 3.7
        The Title
      8. 3.8
        Authors
      9. 3.9
        Acknowledgement
      10. 3.10
        References
      11. 3.11
        Supporting Information
      12. 3.12
        Appendix
    4. General Rules and Use of Language
      1. 4.1
        Basic rules
      2. 4.2
        Scientific language
      3. 4.3
        Choice of the correct word or phrase
      4. 4.4
        Articles
      5. 4.5
        Comparisons
      6. 4.6
        Parallelism