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

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

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

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

- Second Quantization
- Mathematics for Quantum Chemists
- Presentation Techniques in Chemistry - How to write a paper? How to give a seminar?
- Introduction into the use of quantum chemical programs.
- Symmetry and Group Theory
- Molecular Modeling and Drug Design
- Reaction Dynamics
- Time Dependent Methods
- Basic Quantum Mechanics
- Relativistic Methods
- 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:

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

- Computers in Chemistry - Computational Chemistry
**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.**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.**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.**Computational Chemistry I:**Computer assisted structure elucidation; Chemometrics; Computer assisted synthesis; artificial intelligence; special data bases; CAS-ONLINE.**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.**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.**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.**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.**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.).**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.- Concepts and Models in Chemistry - MO Theory
- Atomic and Molecular orbitals (basic facts from MO theory; representation of orbitals; energy diagrams; LCAO-MO approach).
- 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).
- Structure of Molecules (Principle of maximum overlap; hybridization; bond orbitals; VSEPR model; the direct valence model).
- Mulliken-Walsh MO model (Walsh diagrams for AHn (n = 2,3,4), HAB, H2AB, HnAAHn (n=1,2,3) molecules).
- PMO Model (basic formulas; 1,2,3,4-electron cases; first and second order Jahn-Teller effects).
- Hückel MO model (s-p-separation; Hückel theory; aromaticity concept).
- Classical Mechanics applied to chemistry (concepts of strain; molecular mechanics; heats of formation from group increments; molecular modeling).
- Interactions between orbitals (hyperconjugation; anomeric effect; through-space and through-bond interactions; homoconjugation and homoaromaticity; spiroconjugation).
- 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).
- Theory of Pericyclic reactions (The Woodward-Hoffmann rules: orbital symmetry analysis; cycloadditions; electrocylic reactions; sigmatropic rearrangements; cheletropic reactions).
- Evans-Dewar-Zimmermann concept (Evans principle; hückel and Möbius systems; Dewar-Zimmermann rules)
- Hypervalent Molecules (orbitals and bonding; pseudorotation in AH5).
- Transition metal chemistry: Basic Facts and Important Terms (nomenclature; role of transition metal complexes in chemical industry; generalized MO diagrams and electron counting rules).
- ML6, ML5 and ML4 Complexes (octahedral ML6 complexes; high spin and low spin complexes; square planar and tetrahedral ML45n complexes in Biochemistry).
- MLn Fragments (Lego-principle of MO diagrams; ML2, ML3, ML4, and ML5 fragments and their orbitals).
- MCp and MCp2 Complexes (CpML3 complexes; CpM fragment orbitals; metallocenes).
- The isolobal Analogy (isolobal fragments; cluster orbitals; capped annulenes; Wade rules).
- Applied Quantum Chemistry
- 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.
- The wave equation: differential equations; separation of variables.
- The Schrödinger equation and simple applications such as the particle in the box.
- Basic Quantum Mechanics: state of a system; operators and observables; postulates and general principles of quantum mechanics.
- The Harmonic oscillator: diatomic molecules; solution of the harmonic oscillator problem; quantum mechanical tunneling.
- From one to three dimensions: particle in the 3-dimensional box; the rigid rotator; the hydrogen atom; quantum numbers; orbitals.
- Approximated methods: independent particle approximation; variational method; perturbation theory.
- 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.
- 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.
- Hartree-Fock theory: Fock operator; HF equations; LCAO-ansatz; Roothaan-Hall equations; SCF.
- Ab initio theory: STF and GTF; basis sets; RHF and UHF; electron correlation; CI, MBPT, CC, MCSCF.
- Semiempirical methods: p-methods; Valence electron methods: extended Hückel; NDO methods; CNDO, INDO, MINDO, MNDO, AM1, PM3; use of semiempirical methods.
- Computer Assisted Drug Design and Molecular Modeling
- Drug Discovery and Drug Design
- 1.1What is a drug?
- 1.2The role of drugs in the practice of medicine
- 1.3The role of Pharmaceutical Chemistry
- 1.4The history of Pharmaceutical Chemistry
- 1.5Natural substances as drugs, Opium, Quinine, Glycosides, Aspirin, Alkaloids
- 1.5.1Paradigm shifts in medicine
- 1.6Modern drug design: What requirements must a drug fulfill?
- 1.7Stages and cost of modern drug design
- 1.8Tools and teams in modern drug design
- 1.9The role of Computational Chemistry in drug design
- 1.11Drug Discovery - Filtering out Failures
- 1.12Advertisements in the area of CADD
- Computer Assisted Drug Design (CADD)
- 2.1What is CADD? - Explanation of some basic terms
- 2.2Pharmacophore, Lock-Key principle and induced fit theory
- 2.2.1100 years of the Lock-Key Principle
- 2.2.2The Lock-key Principle and the Induced Fit Theory
- 2.2.3The nature of pharmacophores
- 2.2.4Molecular Flexibility
- 2.2.5Identification of pharmacophores
- 2.2.6Searching for pharmacophores
- 2.3Molecular Recognition and Molecular Docking
- 2.4What makes a compound bioactive?
- 2.5The objects of CADD and Molecular Modeling
- 2.6What are the driving forces of Receptor-Drug interactions?
- 2.7Solvent modeling - the role of water
- 2.7.1Properties of water
- 2.7.2Water as a solvent: Aqueous solutions
- 2.7.3Hydrophilic compounds
- 2.7.4Hydrophobic compounds
- 2.7.5Amphiphatic compounds
- 2.8The dynamic aspect of modeling
- 2.9How did CADD develop?
- 2.10What are the techniques and concepts used in CADD and Molecular Modeling?
- 2.11Disciplines and fields contributing to CADD and Molecular Modeling
- Molecular Mechanics (MM)
- 3.1Basic considerations concerning force fields
- 3.1.1Spectroscopic force fields
- 3.1.2The diatomic case
- 3.1.3Vibrations of polyatomic molecules
- 3.2The concept of the force field in MM: historical development
- 3.3Transferability of force fields
- 3.4The energy expression in MM
- 3.4.1Bond stretching potential
- 3.4.2Angle bending potential
- 3.4.3Inversion or out-of-plane bending potential
- 3.4.4Inversion or out-of-plane bending potential
- 3.5Non-bonded interaction potential
- 3.5.1Electrostatic interaction potentials
- 3.5.2Interaction between bond dipole moments
- 3.5.3Calculation of electrostatic interactions
- 3.5.4How to get partial charges?
- 3.5.4.1Charges from electronegativities (Sanderson)
- 3.5.4.2Gasteiger-Marsili charges
- 3.5.4.3Charges from Molecular Dipole moments
- 3.5.4.4Charges from quantum chemical calculations
- 3.5.5Dispersion and exchange repulsion interactions
- 3.5.6Model potentials for van der Waals interactions
- 3.5.7Spherical and non-spherical atoms
- 3.5.8The van der Waals (vdW) radius
- 3.5.9Parametrization of vdW potentials
- 3.6H-bonding
- 3.6.1H-bonding potentials
- 3.7Cross term potentials
- 3.7.1Stretch-bend cross term potential
- 3.7.2Other cross term potentials
- 3.8Parametrization of a Force Field
- 3.8.1Parameter optimization
- 3.9Force field energies V
- 3.9.1Some Basic considerations Concerning Energies
- 3.9.2Molecular Mechanics Calculation of heats of formations
- 3.10Determination of energy and geometry
- 3.10.1Newton-Raphson Method
- 3.10.2Quasi-Newton Methods; Davidon-Fletcher-Powell
- 3.10.3Steepest descent method
- 3.10.4Conjugate gradient method
- 3.10.5Univariate Search Method
- 3.10.6Overview over Optimization Methods
- 3.11Differences between spectroscopic and MM force fields
- 3.12Classification of force fields
- 3.13List of force fields presently in use
- 3.14Generic Force Fields
- 3.15Treatment of long range Coulomb Forces
- 3.16Applicability and limitations of a MM approach
- 3.17Extension of MM; Description of p-conjugated molecules
- 3.18QM/MM methods
- 3.18.1How does a QM/MM method work?
- 3.18.2The junction between the QM and MM regions
- 3.18.3Implementation of the QM/MM approach
- 3.18.4Applications of QM/MM
- Simulation of Macroscopic Properties
- 4.1Basic terms from statistical mechanics
- 4.1.1Concept of the ensemble
- 4.1.2Collection of formulas
- 4.2Searching phase-space and generating an ensemble
- 4.2.1Overview over methods
- 4.2.2Systematic search methods
- 4.3Monte Carlo (MC) methods (Random Methods I)
- 4.3.1Monte Carlo Integration: Hit and Miss
- 4.3.2Random number generators
- 4.3.3Sample mean integration
- 4.3.4Importance sampling
- 4.3.5Sampling error
- 4.3.6Metropolis MC method
- 4.4Random methods without V: Distance Geometry and NMR Spectroscopy (Random methods II)
- 4.4.1Nuclear Overhauser Effect (NOE)
- 4.4.2Karplus Curves and NMR spin-spin coupling constants
- 4.4.3Basic considerations concerning DG
- 4.4.3.1Distance constraints
- 4.4.3.2DG methods: Embedding and metric matrix method
- 4.4.3.3The Metric Matrix method
- 4.4.3.4Triangle Inequality Bounds Smoothing
- 4.4.3.5Metrization
- 4.4.3.6Refinement
- 4.4.3.7Chiral constraints and the chiral error function
- 4.4.3.8Four-dimensional refinement
- 4.4.3.9Minimization
- 4.5MD simulation methods
- 4.5.1Basic considerations
- 4.5.2Practical Aspects of a MDS calculation
- 4.5.2.1Choosing the initial configuration
- 4.5.2.2Choosing the time step
- 4.5.2.3Choosing the initial velocities
- 4.5.2.4Checking the MDS calculation
- 4.5.2.5Checking equilibration
- 4.5.3Verlet method
- 4.5.4Leapfrog method
- 4.5.5Constrained Verlet: SHAKE method
- 4.5.6Different types of MDS
- 4.5.7Constant-T methods
- 4.5.7.1Weak coupling methods
- 4.5.8Constant-P methods
- 4.5.8.1Weak coupling methods
- 4.5.9Stochastic dynamic simulations
- 4.5.10Boundary conditions
- 4.5.10.1Vacuum boundary conditions
- 4.5.10.2Periodic boundary conditions
- 4.5.10.3Extended wall region boundary conditions
- 4.5.11Quantities calculated
- 4.5.12Radial Distribution function
- 4.5.13Calculation of time-dependent properties
- 4.5.14History of MDS
- 4.6Calculation of the Free energy
- 4.6.1Why is it difficult to calculate A, G, and S?
- 4.6.2The coupling parameter approach
- 4.6.3The Thermodynamic perturbation method
- 4.6.4The Thermodynamic integration method
- 4.6.5The potential of mean force
- 4.6.6Free energy differences and the thermodynamic cycle
- 4.6.7Beyond the free energy: Entropy and enthalpy
- 4.6.8Practical considerations
- 4.6.9Recommendations
- Molecular Modeling and Molecular Graphics
- 5.1Historical overview
- 5.2Development of computer graphics
- 5.3Graphical representation of molecules: Standard models
- 5.4Graphical representation technologies
- 5.5Simplified molecular representations
- 5.6Molecular surfaces and volumes
- 5.6.1Corey-Pauling-Koltun (CPK) or van der Waals surface
- 5.6.2The Solvent accessible surface (SAS)
- 5.6.3Solvent excluded surface - Conolly surface
- 5.6.4Surfaces of macromolecules
- 5.6.5The electron density surface
- 5.6.6Channel surface and separating surface
- 5.7Molecular volume
- 5.7.1Packing defects in the protein interior
- 5.7.2Voroni Polyhedra (Dirichlet cells): Protein packing density
- 5.8Molecular superposition and molecular similarity
- 5.8.1Manual approach (Flexible superposition)
- 5.8.2Atom based methods (DISCO and SQ)
- 5.8.3Molecular similarity: Field based methods
- 5.9Molecular skin
- 5.10Mapping of information on molecular surfaces
- 5.10.1The lipophilicity potential
- 5.10.2The electrostatic potential
- 5.11Molecular shape descriptors
- 5.11.1Surface Topology Index
- 5.11.2Flexibility of the surface
- 5.12Examples of modern molecular graphics
- Conformational Analysis
- 6.1Conformations of biomacromolucules
- 6.1.1Primary, secondary, tertiary, and quaternary structure of proteins
- 6.1.2Details of Protein structure (Appendix to 6.1.1)
- 6.2Systematic search methods
- 6.2.1Tree search methods
- 6.2.2Model-building approaches
- 6.3Random search methods
- 6.3.1Genetic algorithms
- 6.3.2Distance geometry
- 6.3.3Metropolis Monte Carlo
- 6.4MDS-based methods
- 6.4.1Simulated annealing (SA)
- 6.4.2Structure refinement by simulated annealing
- 6.4.3Crystallographic refinement
- 6.4.3.1Structure factor and electron density
- 6.4.4NMR structure refinements
- Chemometrics
- 7.1Orgin and current status
- 7.2Multivariate Data
- 7.2.1Definitions
- 7.2.2Organization and classification of data
- 7.2.3Preprocessing
- 7.2.4Distances between objects
- 7.2.5Latent variables
- 7.3Linear Methods
- 7.3.1Projection of multivariate data
- 7.3.2Principal component analysis (PCA)
- 7.3.3Multiple linear regression (MLR) and principle component regression (PCR)
- 7.3.4Partial least squares method (PLS)
- 7.4Non-linear methods
- 7.4.1An example for non-linear models
- 7.5Modeling methods
- 7.5.1SIMCA principle component modeling
- 7.5.2Classification methods
- 7.5.2.1Probability density classification (Bayes strategy)
- 7.5.2.2K nearest-neigbor classification (KNN)
- 7.5.3Factor analysis
- 7.5.4Cluster analysis
- 7.5.5Linear discriminant analysis (LDA)
- 7.6Validation tools
- 7.6.1Cross-validation
- 7.6.2Bootstrapping
- 7.6.3Frequently used statistical indices
- 7.6.4Cross-validation in PLS
- 7.6.5Chance effects and chance correlation
- Artificial Neural Networks (ANN)
- 8.1Background and basics of ANN
- 8.2What can neural networks do?
- 8.2.1Artificial neuron
- 8.2.2Net input, net and weight
- 8.2.3How to get the best weights?
- 8.2.4Transfer functions in neurons
- 8.2.5Bias
- 8.2.6Linking neurons to networks
- 8.3Architecture
- 8.4The Kohonen network
- 8.4.1Special characteristics
- 8.4.2Competitive learning
- 8.4.3An example: mapping from 3 to 2 dimensions
- 8.4.4Summary
- 8.5Counterpropagation
- 8.5.1Supervised competitive learning
- 8.5.2Summary
- 8.6Error-backpropagation learning
- 8.6.1Architecture
- 8.6.2Learning by back propagation
- 8.6.3Learning algorithm
- 8.6.4Essentials
- 8.7When is the training finished?
- 8.7.1Overtraining
- 8.8Applications of ANNs in Drug design
- 8.8.1ANN in Quantitive structure activity relationships
- 8.8.2ANN to determine the secondary structure of proteins
- 8.8.3Kohonen maps of the electrostatic potential
- Lipophilicity
- 9.1Factorization of molecular lipophilicity
- 9.21D-approaches for calculating partition coefficients
- 9.2.1Substituent constants of Hansch and Fujita
- 9.32D-appraoches for calculating partition coefficients
- 9.3.1Methods based on fragmental constants and correction factors
- 9.3.2Method of Leo and Hansch (CLOGP)
- 9.3.3Klopman's method (CASE)
- 9.3.4Methods based on fragmental constants only
- 9.3.4.1Method of Suzuki and Kudo (CHEMICALC)
- 9.3.4.2Method of Broto, Moreau and Vandycke (ALOGP)
- 9.3.5Methods based on global two-dimensional structural properties
- 9.3.5.1Calculation of peptide lipophilicity
- 9.3.5.2Calculation of lipophilicity using structural parameters
- 9.43D- approaches for calculating partition coefficients
- 9.4.1Solvent-accessible surface areas (SASA)
- 9.4.2MO calculations and Bodor's method (BLOGP)
- 9.4.3Methods based on molecular fields: the lipophilicity potential (MLP)
- 9.54D- approaches for calculating partition coefficients
- 9.5.1Methods based on an ensemble of conformers
- 9.5.2Methods based on direct computation
- 9.5.3Methods based on a continuum solvation model
- 9.5.4Methods based on free energy perturbation methods
- 9.6Comparison of the accurary of different methods
- 9.7Examples from drug design
- 9.7.1log P as a tool to unravel intramolecular interactions
- 9.7.2log P values in 2D-QSAR
- 9.8Summary of computer programs
- 9.9Concluding remarks
- 2D-Quantitative Structure-Activity Relationship (2D-QSAR)
- 10.1Definition
- 10.2QSAR methodology
- 10.2.1Historical background
- 10.3Basic concepts of QSAR
- 10.3.1Hansch analysis
- 10.3.2Free-Wilson analysis
- 10.3.3An example: Adrenergic activities of N,N-di-methyl-a bromopheneythlamines
- 10.3.4Summary
- 10.4Molecular descriptors
- 10.4.1Electronic parameters
- 10.4.2Polar interactions
- 10.4.3Steric parameters
- 10.4.4Topological parameters
- 10.4.5Quantum-chemical descriptors
- 10.5Biological parameters
- 10.62D-QSAR in drug design
- 10.6.1Transport and distribution of drugs in biological systems
- 10.6.2Enzyme inhibition
- 10.6.3Model system for cysteine protease
- 10.6.4Prediction of mutagenic potencies
- 10.6.5QSAR for antimalarical compounds
- 10.6.6b
_{1}- and b_{2}- antagonist activities - 10.6.7Activity-activity relationships
- 10.7Validation of QSAR models
- 10.8Conclusions
- 3D-QSAR; Comparative Molecular Field Analysis (CoMFA) and - Similarity Analysis (CoMSIA)
- 11.13-QSAR
- 11.2Assumptions in 3D-QSAR
- 11.3CoMFA methodology
- 11.4Steps of a CoMFA analysis
- 11.4.1Pharmacophore hypothesis and alignment
- 11.4.2Superposition of all molecules
- 11.4.3Box, Grid size and 3D field calculations
- 11.4.4CoMFA Data Table
- 11.4.5Derivation of the CoMFA model
- 11.4.6CoMFA coefficient maps
- 11.4.7Validation of results
- 11.5An example: CBG and TBG binding affinities of steroids
- 11.6CoMFA application in drug design, overview
- 11.7Conclusions on CoMFA
- 11.8Comparative molecular similarity analysis (CoMSIA)
- 11.8.1Definition of similarity indices
- 11.8.2Similarity fields
- 11.9An example benzamidine inhibitors binding to trypsin, thrombin, and factor Xa
- CADD: Methods and Strategies
- 12.0.1The drug development process (target oriented)
- 12.1Lead discovery
- 12.2Irrational drug design and combinatorial chemistry
- 12.2.1The combinatorial explosion of chemistry
- 12.2.2What is combinatorial chemistry
- 12.2.3Merrifield's synthesis of peptides
- 12.2.4CombChem: Mix-and-split libraries
- 12.2.5Historical development of CombChem
- 12.3Virtual screening
- 12.3.1Setting up a virtual library
- 12.3.2Practical considerations: Encoding of the library
- 12.3.3The virtual screening process
- 12.3.42D-similarity: Tanimoto coefficients
- 12.3.5Clustering (=pooling) of structures
- 12.3.6Virtual screening: 3D similarity
- 12.3.7Reduction and diversity of a virtual library
- 12.3.8Data mining
- 12.4Structure-based ligand design: Pharmacophore generation
- 12.4.1Structure-based ligand design
- 12.4.2Determination of a pharmacophore
- 12.4.3The active analog approach (AAA)
- 12.4.4Ensemble distance geometry
- 12.4.5Ensemble molecular dynamics
- 12.4.6Pharmacophores by clique detection
- 12.4.7Pharmacophore representation
- 12.5Molecular recognition
- 12.6Molecular docking
- 12.7De Novo design of ligands
- 12.7.1Analysis of the receptor: Generation of a constraints model
- 12.7.1.1The GRID program
- 12.7.1.2The Multiple-Copy Simultaneous Search (MCSS) method
- 12.7.1.3The Program LUDI
- 12.7.2Structure generation methods
- 12.7.2.1The outside-in (linking) approach: LUDI
- 12.7.2.2The linking part
- 12.7.2.3Creating real molecules
- 12.7.2.4The inside-out (building) approach: GROW
- 12.7.2.5Program LEGEND
- 12.7.3Structure evaluation
- 12.7.4When does one use de Novo design?
- 12.7.5Practical advice on the application of de Novo design methods
- 12.7.6De Novo design: Conclusions and future perspectives
- 12.8Petides and peptide analogs as drugs: Peptidomimetics
- 12.8.1Peptidomimetics
- 12.8.2Design of peptidomimetics: the CAVEAT program
- Protein Modeling
- 13.1The Protein Data Bank (PDB)
- 13.2Relationship between sequence and 3D structure of a protein
- 13.3Alignment of protein sequences
- 13.3.1Needleman-Wunsch alignment method
- 13.3.2Multiple sequence alignments (MSA)
- 13.3.2.1Construction of the core
- 13.3.2.2Construction of loops and turns
- 13.3.2.3Construction of the Side chains
- 13.3.2.4Refinement of the homology model
- 13.4Homology modeling of proteins
- 13.5Prediction of protein structures by threading
- 13.6Comparison of various strategies in homology modeling
- 13.7Protein folding
- 13.7.1Thermodynamics of protein folding
- 13.7.2Levinthal's paradox and the kinetics of protein folding
- Present and Future Perspectives of Drug Design
- 14.1Successes of CADD
- 14.2Genetechnology and drug design
- 14.3Bioinformatics
- 14.4Future developments
- 14.4.1Improvements of force fields
- 14.4.2Integration of quantum chemical methods, better QC/MM methods
- 14.4.3Better methods for DG calculations
- 14.4.4ADME modeling
- Ab initio Methods I: Hartree-Fock Theory
- Introduction
- 1.1What are ab initio calculations?
- 1.2Goals of ab initio quantum chemistry
- 1.3Criteria for ab initio methods
- 1.4Approximations and limitations
- 1.5What is calculated?
- 1.6Classification of methods used in Computational Chemistry
- 1.7Acronyms, units, symbols
- 1.8History of ab initio Quantum Chemistry
- 1.9What ab initio programs are available
- 1.10What ab initio programs are available
- The independent particle model
- 2.1Some useful basics from quantum mechanics
- 2.2The independent particle model
- 2.3Hartree product versus Slater determinant
- 2.4Determination of the normalization constant
- 2.5Matrix Elements over Slater determinants - Slater-Condon rules
- 2.5.1One electron operators
- 2.5.2Two electron operators
- 2.6Simplification of the Hamiltonian to an effective One-electron operator
- 2.6.1Hartree Fock (HF) energy formula
- 2.7Hartree Fock Equations
- 2.8LCAO-Ansatz to solve the HF equations - Roothaan-Hall equations
- 2.9Calculation of the energy according to Roothaan-Hall
- What is needed for a Hartree-Fock (HF) calculation?
- 3.1Flow chart for a HF calculation
- 3.2Input for a HF calculation
- 3.2.1Specification of the molecule
- 3.2.2Molecular geometry
- 3.2.2.1Cartesian versus internal coordinates
- 3.2.2.2The z-matrix formalism
- 3.2.2.3Special coordinates - puckering parameters
- 3.3How to find the right number of coordinates?
- 3.3.1Determination of molecular point group in an ab initio program
- 3.3.2Number of independent coordinates for symmetric molecules
- 3.4The molecular framework group
- 3.5What ab initio programs are available?
- The basis functions
- 4.1The building block principle of MO theory
- 4.2Hydrogen type functions and Hydrogen type orbitals
- 4.3Slater type functions (STF) and Slater type orbitals (STO)
- 4.4Slater rules for zeta values
- 4.5Gaussian type functions (GTF) and Gaussian type orbitals (GTO)
- 4.5.2Energy of the ground state of H
- 4.5.3Comparison of HF, Slater, and Gaussian orbitals
- 4.5.4Cartesian Gaussian functions
- 4.5.5Gaussian lobe functions
- 4.6Summary
- The basis set
- 5.1How to use basis functions?
- 5.2Notation for basis sets
- 5.3Minimal basis sets (MBS, SZ)
- 5.4Double Zeta basis sets (DZ)
- 5.5Split-valence basis sets (VDZ)
- 5.6Extended Basis sets: TZ, QZ, PZ
- 5.7Augmented basis sets
- 5.7.1Floating basis functions
- 5.7.2Bond functions
- 5.7.3Polarization functions
- 5.8Uncontracted and contracted basis sets
- 5.8.1Contraction of a (7s3p) basis for N
- 5.8.2Notation for contracted basis sets
- 5.8.3Rules for getting contracted basis sets
- 5.8.4General contraction schemes
- 5.9Pople's minimal basis sets
- 5.9.1Scaling theorem
- 5.9.2STO-NG minimal basis sets
- 5.10Pople's split valence and augmented split valence basis sets
- 5.11Special Basis sets
- 5.11.1Augmented basis sets with diffuse functions
- 5.11.2Even-tempered basis sets
- 5.12Selection of an appropriate basis set for a given problem
- 5.12.1What is available?
- 5.12.2How to select a basis set?
- 5.12.3Pople's recipe
- 5.12.4How to get basis sets for high accuracy calculations?
- 5.12.5What basis set is needed for what property?
- Calculation of integrals
- 6.1Notation for electron integrals
- 6.2Number of integrals
- 6.3Properties of GTFs relevant for integral calculations
- 6.3.1Basics
- 6.3.2Gaussian Product Theorem
- 6.3.3The Laplace Transform of r12-1
- 6.3.4The Transfer equation
- 6.3.5Differentiation and recurrence relationships
- 6.3.6Gaussian Quadrature
- 6.4Overlap integrals
- 6.5Kinetic energy integrals
- 6.6Nucleus-electron attraction integrals
- 6.7Evaluation of two-electron repulsion integrals (ERIs)
- 6.7.1Evaluation of the [ss|ss] ERI
- 6.7.1.1Prescreening of ERIs
- 6.7.2McMurchie-Davidson scheme
- 6.7.3Dupuis-King-Rys scheme
- 6.7.4Pople-Hehre calculation of ERIs
- 6.7.5The PRISM algorithm
- 6.8The Resolution of the identity (RI) method
- 6.9Storage of ERIs
- Solution of the Self-Consistent Field (SCF) problem
- 7Solution of the SCF Problem
- 7.1Conventional Roothaan-Hall SCF
- 7.2Initial Guess
- 7.2.1Available methods for setting up the initial guess
- 7.2.2Improvement of starting orbitals - Basis set expansion
- 7.2.3Reuse of other wave-functions
- 7.3Solution of the pseudo-eigenvalue problem
- 7.4Orthogonalization procedures
- 7.4.1Schmidt procedure - successive orthonormalization
- 7.4.2Löwdin procedure
- 7.4.3Comparison of orthonormalization procedures
- 7.4.4Comparison between nonorthogonal and orthogonal basis set descriptions
- 7.5Diagonalization procedures
- 7.6Stationary state conditions for the SCF
- 7.7Construction of the Fock matrix
- 7.7.1Raffenetti ordering
- Convergence of SCF calculations
- 8.1General aspects: Convergence and convergence problems
- 8.1.1What to do in case of convergence problems?
- 8.2Univariate search methods and state loyalty
- 8.2.1Pople-Seeger method
- 8.2.2State loyalty by the Pople-Seeger method
- 8.2.3Camp-King method
- 8.2.4Implementation of the Camp-King method
- 8.3Extrapolation methods
- 8.3.1Damping
- 8.3.2Dynamic damping
- 8.3.3Aitken method
- 8.3.4Roothaan-Bagus-Sack method
- 8.4Level shifting
- 8.5Direct inversion of the iterative subspace (DIIS)
- 8.5.1Precursors of DIIS
- 8.5.2Practical aspects of DIIS
- 8.5.3Extension of DIIS: ADEM-DIOS
- 8.6Quadratically convergent SCF (QC-SCF)
- 8.6.1Linear and quadratic convergence
- 8.6.2QC-SCF method
- 8.6.3Comparison with normal SCF
- 8.6.4Implementation of QC-SCF in an ab initio program
- 8.7Overview of starting and terminating convergence methods
- SCF for open shell cases
- 9.1Derivation of a minimum condition for restricted open shell cases - generalized Brillouin theorem
- 9.2Generalized restricted open shell theory
- 9.2.1General derivation and relationship to MCSCF
- 9.2.2Derivation of the pseudo-eigenvalue equations
- 9.2.3LCAO Ansatz for ROHF - Generalized Roothaan-Hall equations
- 9.2.4Coupling coefficients aIJ and bIJ
- 9.3Partitioned HF (PHF)
- 9.4Roothaan's ROHF
- 9.5McWeeny' ROHF
- 9.6Unrestricted HF theory (UHF)
- 9.6.1Pople-Nesbet equations
- 9.6.2Properties of the UHF energy
- 9.6.3The dissociation problem
- 9.6.4The UHF wave-function
- 9.6.5Spin projection methods
- 9.6.5.1Spin constraint UHF (SUHF)
- 9.6.6UHF electron density and spin density distribution
- 9.6.7Calculation of hyperfine coupling constants
- General HF Theory
- 10.1Constraints to complex GHF
- 10.2Stability tests
- 10.2.1Singlet instability
- 10.2.2Non-singlet instabilities
- 10.3Complex HF (CHF)
- 10.3.2Necessity of using complex HF - the O2 example
- 10.3.1Form of complex orbitals
- 10.3.2Roothaan Hall for CHF
- Direct SCF methods for large molecules
- 11.1Number of ERIs for large molecules
- 11.2Flow chart for a DSCF program
- 11.3Prescreening of ERIs and neglecting of ERIs
- 11.4Recursion formula for the Fock matrix
- 11.5Selective storage of ERIs - Semi-direct SCF
- 11.6Error progression in a DSCF
- 11.7DSCF calculations for large molecules
- Ab Initio Methods II: Electron Correlation Methods (CI and Perturbation Theory)
- Why do we need correlation corrected methods?
- 1.1Shortcomings of the HF approach
- 1.2What is correlation?
- Electron Density Functions: Density Matrices
- 2.1Reduced density matrices
- 2.2Energy in terms of Gp - N-representability problem
- 2.3Pair density distribution
- 2.4Fermi hole and Coulomb hole
- 2.5Density matrices in HF theory - Fock-Dirac density matrix
- 2.6Pictorial display of electron correlation
- Definition of the Correlation Energy
- 3.1Magnitude of the correlation energy
- 3.2Correlation energies from experimental data
- Types of Electron Correlation
- 4.1Static and dynamic electron correlation
- 4.2Electron Pair correlation
- 4.3Left-right, angular, in-out correlation
- 4.4Intraatomic and interatomic correlation
- 4.5Internal and external correlation
- 4.6Higher correlation effects and higher excitations
- What Correlation methods are available?
- General Considerations
- 1.1How many terms are in the full CI wave function
- 1.2CI matrix
- 1.3Calculation of the CI correlation energy
- Full CI for H2
- Truncated CI: CID and CISD
- Conventional CI calculations
- 4.1Integral transformation
- 4.2Construction of spin-adapted CSF
- 4.3Calculation of matrix elements
- 4.4Diagonalization methods: Nesbet method, Davidson method
- Direct CI
- 5.1Multipurpose direct CISD
- 5.2A CISD program
- Correlation Orbitals - Natural Orbitals
- 6.1Correlation orbitals
- 6.2Natural orbitals
- 6.3Calculation of natural orbitals
- 6.4Natural orbitals of H
_{2}O - 6.5Iterative natural orbital method
- Basis sets for correlation calculations
- 7.1Repetition of some basic terms
- 7.2Pople's basis sets
- 7.3Dunning's correlation consistent basis sets
- 7.4ANO basis sets
- 7.5Dual basis sets
- Error consistency
- 8.1Basis set error consistency: truncation error and BSSE
- 8.2BSSE (counterpoise method; inter- and intramolecular BSSE)
- 8.3Method error consistency: correlation error and size-extensivity error
- 8.4Size-extensivity - Size-extensivity versus size-consistency
- 8.5Size-extensivity error of CI
- 8.6Size-extensivity corrections: Davidson correction, Pople correction
- Rayleigh-Schrödinger Perturbation Theory
- 1General perturbation theory formulas, intermediate normalization, E(0) representation, second order, third order, fourth order corrections
- Møller-Plesset Perturbation Theory
- 2.1First order correction to the energy Eorb
- 2.2Second order correction to the energys
- 2.3First order correction to the wave function
- 2.4Third order correction to the energy
- 2.5The original MP perturbation operator
- Epstein-Nesbet Perturbation Theory
- 3.1The EN perturbation operator
- 3.2Second order correction to the energy
- 3.3Advantages and disadvantages of EN perturbation theory
- Diagrammatic Perturbation Theory
- 4.1Introduction to diagrams
- 4.2Hugenholtz diagrams
- 4.3Goldstone diagrams rules, calculation of second order and third order energy
- 4.4Brandow diagrams
- 4.5How many diagrams exist at MBPTn?
- General Perturbation Theory
- 5.1Feshbach operator
- 5.2Brillouin-Wigner Perturbation Theory
- 5.3Resolvent expansion of energy and wave function
- 5.4General Rayleigh-Schrödinger Perturbation Theory
- 5.5Fourth order MP Theory (derivation of the energy formula)
- 5.6General MPn Theory (MP5, MP6, etc.)
- Dependence on the number of particles
- 6.1Investigation of first, second, and third order energy
- 6.2Size-extensivity of MP energies
- 6.3Linked 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.
- 6.4Linked Diagram Theorem
- 6.5Characterization of diagrams
- Convergence of the MPn series
- 7.1Convergence behavior (oscillations, divergence)
- 7.2Convergence radius and intruder states
- 7.3Convergence radius and intruder states
- 7.4Extrapolation procedures: Pade approximants
- 7.5Extrapolation formulas
- 7.6Extrapolation procedures: First order and higher order Feenberg scaling
- Projected MP Theory
- 8.1Annihilation versus projection methods
- 8.2Calculation of <S2> corrections
- 8.3PUHF, PMP2 and PMP3
- 8.4Practical considerations
- Application of MP Theory
- 9.1Cost considerations and feasibility
- 9.2Programming considerations
- 9.3Electron density analysis of MP response densities
- 9.4MP geometries
- 9.5MP energies
- 9.6MP dipole moments and other first order properties
- 9.7MP frequencies and IR intensitie
- 9.8Advantages and disadvantages of MP theory
- Greens Functions
- 10.1One-particle Green's functions
- 10.2One-particle Green's functions for an N-electron system
- 10.3Calculation of ionization potentials and electron affinities
- 10.4How to solve the Dyson equation?
- 10.5Relationship between the Green's function method and perturbation theory
- 10.6Application of Green's functions
- Ab initio Methods III: Electron Correlation Methods (From Single to Multi Configuration methods)
- Basic Concepts - A repetition
- 1.1Time-dependent Schrödinger Equation
- 1.2Born-Oppenheimer Approximation
- 1.3Variational Methods for ground and excited states
- 1.4Size consistence and size-extensiveness
- Single reference - multi determinant problems
- 2.1Reference, Configuration, and Determinant
- 2.2General ROHF
- 2.2.1Generalized Brillouin Theorem
- 2.2.2Generalized HF Equations
- 2.2.3Generalized Roothaan Hall Equations
- 2.3The Low-Spin Open Shell Problem
- 2.3.1ROSS
- 2.3.2ROHF-MP
- 2.4From ROHF to MCSCF
- Two-Configuration Descriptions
- 3.1GVB
- MCSCF
- 4.1Energy Expression in MCSCF
- 4.2CI Equations and Generalized Brillouin Theorem
- 4.3Methods to determine the MCSCF wave function
- 4.3.1Super CI Technique
- 4.3.2Quadratically Convergent MCSCF Methods: Newton Raphson Method
- 4.4The H2 molecule
- CASSCF
- Ab Initio Methods V: Calculation of Molecular Properties
- Overview over Molecular Properties
- 1.1Classification 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)
- 1.2Properties 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)
- Ab initio Energies
- 2.1From ab initio Energies to heats of formation
- 2.1.1Correction of heats of formation from T to 0 K
- 2.1.2Calculation of experimental molecular energies
- 2.1.3Calculation of theoretical energies within the Born-Oppenheimer approximation
- 2.1.4Estimation of relativistic effects
- 2.1.5Estimation of correlation energies
- 2.1.6How to get to HF limit energies
- 2.2Practical considerations
- 2.3Direct 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)
- 2.4Heats of formation from ab initio Energies: The G Theoretical Model Chemistry
- 2.4.1Basis set additivity
- 2.4.2Use of isogyric reactions
- 2.4.3Gaussian1 (G1) Theory
- 2.4.4G2 Theory
- 2.4.5Modifications: G2(MP2) and G2M
- 2.4.6G3 Theory
- 2.5Other ways of calculating heats of formation
- 2.5.1Dewar's approach
- 2.5.2Bond Additivity Corrections (BAC) method
- 2.5.3Transition metal chemistry: PCI80
- 2.6The CBS Theoretical Model Chemistry
- 2.6.1Determination of the SCF limit
- 2.6.2Determination of PNOs
- 2.6.3CBS Pair energies
- 2.6.4CBS-QCI/APNO model
- 2.7Heats of Formation from Formal Reactions
- 2.7.1Bond separation energies and isodesmic reactions
- 2.7.2Homodesmotic reactions and super-homodesmotic reactions
- 2.7.3Resonance and strain energies from homodesmotic reactions
- Interpretation of the wave function
- 3.1Properties of the molecular wave function
- 3.1.1The Hellmann-Feynman theorem
- 3.1.2The virial theorem
- 3.1.3Methods with and without a wave function
- 3.2Orbital energies
- 3.2.1Koopmans theorem
- 3.2.2When does Koopmans theorem apply?
- 3.2.3Excitation energies from orbital energies (Singlet and triplet states)
- 3.2.4Orbital energies and total energy
- 3.3Population analysis
- 3.3.1Mulliken population analysis
- 3.3.2Shortcomings of the Mullkien population analysis
- 3.3.3Improvements of the Mulliken population analysis
- 3.3.4Modified atomic orbitals (MAOs)
- 3.3.5Charges from the electrostatic potential
- 3.3.6Weinhold's natural population analysis: NAOs and NBOs
- 3.4The shape of canonical Molecular Orbitals
- 3.4.1How to read the coefficients of MOs?
- 3.4.2Delocalized and localized MOs
- 3.4.3Graphical representations of MOs
- 3.5Localization of MOs
- 3.5.1Localization criteria
- 3.5.2Boys localization
- 3.5.3Edminston-Ruedenberg localization
- 3.5.4Magnasco-Perico localization
- 3.5.5Pipek-Mezey localization
- Analysis of the electron density distribution
- 4.1Properties of the electron density distribution
- 4.2Difference density distribution
- 4.3Measurement of the electron density distribution
- 4.4Ways of analyzing the electron density distribution
- 4.5Topological analysis
- 4.6Theory of virial subspaces
- 4.6.1Open and closed systems
- 4.6.2Zero-flux surfaces
- 4.6.3Bader's atoms in molecules theory
- 4.6.4Atomic properties
- 4.7The Laplacian of the electron density distribution
- 4.7.1The local virial theorem
- 4.7.2Bond and lone pair concentrations
- 4.7.3The shell structure of the atoms
- 4.8Description of the chemical bond
- 4.8.1The electrostatic description of the chemical bond
- 4.8.2Ruedenberg's description of the chemical bond
- 4.8.3Bader's description of the chemical bond
- 4.8.4Bond order, bond ellipcity, and bond polarity
- 4.8.5A general model of covalent bonds (Cremer-Kraka criteria)
- 4.8.6Bond energies and bond dissociation energies
- 4.8.7Bond strength as related to intrinsic properties of the bond
- 4.8.8Overlap and electronegativity
- Molecular properties from analytical energy derivatives
- 5.1Analytical derivatives in HF theory
- 5.1.1HF first derivatives
- 5.1.2HF second derivatives
- 5.1.3Coupled Perturbed Hartee-Focck (CPHF) theory
- 5.1.4Implementation according to Pople
- 5.1.5The z-vector formalism of Handy and Schaefer
- 5.1.6Overview over RHF and GROHF derivatives
- 5.2MPn derivatives
- 5.3MCSCF and CASSCF derivatives
- 5.4CI derivatives
- 5.5Implementation of derivatives in an ab initio program
- 5.6General response theory
- 5.6.1Expectation value versus response property
- Molecular Geometries and Geometry Optimizations
- 6.1Basic definitions and overview
- 6.2Optimization methods - Coordinate systems
- 6.2.1Coordinates used for optimization (redundant, nonredundant)
- 6.2.2Relationship between internal and Cartesian coordinates: B matrix
- 6.2.3Relationships for redundant coordinates: G and K matrices
- 6.2.4Gradient and forces for non-redundant and redundant coordinates
- 6.2.5Optimization in redundant internal coordinates
- 6.2.6Conversion from redundant internal to Cartesian coordinates
- 6.2.7Advantages of redundant coordinates
- 6.2.8Natural internal coordinates of Pulaty and Boggs
- 6.2.9Delocalized internal coordinates of Baker
- 6.2.10Use of Cartesian coordinates in optimizations
- 6.3Optimization methods - general features
- 6.3.1Use of the Hessian for optimizations
- 6.3.2Convergence criteria
- 6.3.3Stepsize and search direction
- 6.3.4Search for a local minimum
- 6.3.5Search for a transition state
- 6.4Optimization methods - general features
- 6.4.1Non-derivative methods (Univariate search, Simplex method)
- 6.4.2Gradient methods (Steepesct descent, Conjugate gradient methods)
- 6.4.3Quasi-Newton methods (Davidon-Fletcher-Powell, Murtagh-Sargent)
- 6.4.4Newton-Raphson methods
- 6.5Special search techniques
- 6.5.1Minimum search - Schlegel's method
- 6.5.2Transition state searches
- 6.5.3Mode following method of Baker
- 6.5.4Up-hill searches
- 6.5.5Rational functional methods
- 6.6Definition of the molecular geometry
- 6.6.1What is the difference between re, rg, ra, r0, rv, rz?
- 6.6.2Quality of HF geometries
- 6.6.3MP and CC geometries
- 6.6.4DFT geometries
- Conformational processes
- 7.1Basic terms: Conformations and conformers
- 7.2Internal rotation
- 7.2.1Rigid and flexible rotors
- 7.2.2Fourier expansion of the rotational potential
- 7.2.3Rotational barriers and their electronic nature
- 7.2.4Coupled rotors: Fourier expansion and chemical relevance
- 7.3Inversion of molecular conformations
- 7.3.1Inversion barriers and electronic nature
- 7.4Ring puckering and pseudorotation
- 7.4.1The ring puckering coordinates: ring inversion and ring pseudorotation
- 7.4.2Conformational space: Dimension and basis conformations
- 7.4.3The cyclohexane globe and its extensions
- 7.4.4Relationship between acyclic rotors and cyclic pseudorotors
- 7.5Acyclic pseudorotors
- 7.5.1Berry pseudorotation
- 7.6Bond pseudorotation
- Vibrational frequencies and force constants
- 8.1Basic terms: Conformations and conformers
- 8.1.1The vibrational energy levels in the harmonic approximation
- 8.1.2Anharmonic vibration and More potential
- 8.1.3Vibrational selection rules
- 8.1.4Vibration-rotation spectrum
- 8.1.5Raman vibrational spectrum
- 8.2Classical calculation of the normal modes of a polyatomic molecule
- 8.2.1Cartesian vs. internal coordinates: Wilson B matrix
- 8.2.2Mass-weighted coordinates and Wilson G matrix
- 8.2.3The harmonic approximation
- 8.2.4Derivation of the Euler-Lagrange equations
- 8.2.5Generalized force constants and force constant matrix
- 8.2.6Calculation of normal modes in terms of Cartesian and internal coordinates
- 8.3Infrared and Raman spectra
- 8.3.1Vibrational selection rules
- 8.3.2Theory of infrared intensities (harmonic approximation)
- 8.3.3Calculation of IR intensities with HF and correlated methods
- 8.3.4Absolute and relative IR intensities, intensities of isotopomers
- 8.3.5Calculation of the Raman spectrum
- 8.4Determination of local modes
- 8.4.1Isolated stretching modes
- 8.4.2Local modes from overtone spectroscopy
- 8.4.3Adiabatic internal modes (AIMs)
- 8.4.4The properties of AIMs
- 8.5Analysis of vibrational spectra
- 8.5.1Normal mode analysis
- 8.5.2Potential energy analysis
- 8.5.3Characterization of normal modes in terms of AIMs
- 8.5.4Spectra of isotopomers and their calculation
- 8.5.5Correlation of vibrational spectra
- 8.5.6Charges from vibrational intensities
- 8.6Vibrational-rotational coupling
- 8.6.1Coriolis forces
- 8.7The effects of anharmonicity
- 8.7.1Overtones and combination bands
- 8.7.2Fermi resonances
- 8.7.3Calculation of cubic and quartic force constants
- 8.7.4Vibrational corrections of measured geometries
- 8.8The role of force constants for describing bond strength
- 8.8.1Badger rule
- 8.8.2Force constants from experimental spectra
- 8.8.3Force constants and the intrinsic bond dissociation energy
- Ionization potentials
- 9.1Koopmans theorem and its applicability
- 9.2PE and ESCA spectroscopy
- 9.3Explicit calculation of ionization potentals
- 9.4Ionization potentials from Green function methods
- Electric properties
- 10.1The response to electric fields
- 10.1.1Molecular response parameters
- 10.1.2General theory of response properties in an external electric field
- 10.1.3One- and two-electron properties
- 10.2Electric multipole moments
- 10.2.1Dipole moments
- 10.2.2Quadrupole moments
- 10.2.3Higher moments
- 10.2.4Use of multipole moments: Distributed multipole expansion
- 10.3Electric field gradient and nuclear quadrupole coupling constant
- 10.4Electrostatic potential
- 10.5The molecular polarizability
- 10.5.1The static electric polarizability
- 10.5.2Polarizability and molecular properties
- 10.5.3Hyperpolarizabilities
- 10.6Bulk electrical properties
- 10.6.1The relative permittivity and the electric susceptibility
- 10.6.2Polar molecules
- 10.6.3Refractive index and dynamic polarizability
- 10.7Optical activity
- 10.7.1Circular birefringence and optical rotation
- 10.7.2Magnetically induced polarization
- 10.7.3Rotational strength
- Magnetic properties
- 11.1Interactions of magnetic fields with molecules: response properties
- 11.2Diamagnetism and paramagnetism
- 11.2.1Diamagnetism
- 11.2.2Magnetic dipole moment, magnetizability, and magnetic susceptibility
- 11.2.3Paramagnetism
- 11.3Vector functions and their derivatives - a repetition
- 11.3.1Derivatives of vector functions
- 11.3.2The vector potential
- 11.4Description of magnetic properties by perturbation theory
- 11.4.1The perturbed Hamiltonian
- 11.4.2Calculation of diamagnetic and paramagnetic susceptibility
- 11.4.3Diamagnetic and paramagnetic current density
- 11.5Calculation of NMR chemical shifts
- 11.5.1Shielding constants
- 11.5.2Diamagnetic contribution to shielding
- 11.5.3Paramagnetic contribution to shielding
- 11.5.4The GIAO method
- 11.5.5The IGLO method
- 11.5.6The LORG method
- 11.5.7GIAO-MP and other methods
- 11.5.8The IGLO-DFT method
- 11.5.9Results of NMR chemical shift calculations
- 11.5.10Choice of the reference
- 11.5.11The NMR-ab initio-IGLO method
- 11.5.12IGLO-PISA method
- 11.5.13State-of-the-art theory: Relativistic corrections
- 11.6Spin-spin coupling in ESR (Electron Spin Resonance)
- 11.6.1Hamiltonian for electron spin coupling
- 11.6.2Hyperfine splitting constants
- 11.6.3Calculation of the Fermic contact term
- 11.6.4Results of unrestricted versus restricted theory
- 11.6.5Interpretation of ESR spectra
- 11.7NMR spin-spin coupling constants
- 11.7.1Mechanism of spin-spin coupling between nuclei
- 11.7.2The spin-spin coupling Hamiltonian
- 11.7.3Ab initio methods for calculating NMR coupling constants
- 11.7.4DFT methods for calculating NMR coupling constants
- 11.7.5Results obtained with the EOM-CC method
- 11.7.6Karplus curves and determination of molecular conformations
- 11.7.7Longe range coupling constants
- 11.7.8Relationships between coupling constants and other molecular quantities
- Excited states of molecules
- 12.1Excited states of a diatomic molecule - a repetition
- 12.1.1Coupling of angular momentum: Hund coupling
- 12.1.2Selection rules
- 12.1.3Vibronic transitions: Franck-Condon principle
- 12.2Electronic spectra of polyatomic molecules
- 12.2.1Chromophores
- 12.2.2Vibronically allowed transitions
- 12.2.3Singlet-triplet transitions
- 12.2.4Non-radiative decay
- 12.2.5Radiative decay: Fluorescence and phosphorescence
- 12.2.6Intersystem crossing
- 12.3Ab initio methods for calculating excited states
- 12.3.1General problems of calculating excited states
- 12.3.2The CIS method and its extensions
- 12.3.3CASSCF and CAS-PT2
- 12.3.4EOM-CC methods
- 12.3.5DFT for excited states
- Molecular interactions and molecular solvation
- 13.1Weak molecular interactions: van der Waals complexes
- 13.2Forces acting in van der Waals complexes
- 13.2.1Electrostatic interactions between molecules
- 13.2.2Induced electrostatic interactions
- 13.2.3Polarizability and dispersion forces
- 13.2.4Overlap or exchange repulsion
- 13.3Binding energies and geometries of van der Waals complexes
- 13.3.1Basis set and method requirements
- 13.3.2Basis set superposition error and counterpoise method
- 13.3.3Failure of DFT
- 13.3.4Typical binding energies and geometries
- 13.4Perturbation theory for intermolecular forces
- 13.4.1Short-range perturbation theory
- 13.4.2Symmetry-adapted perturbation theories
- 13.4.3First order and second order terms
- 13.5Electron density description of van der Waals complexes
- 13.5.1Difference densities and Laplace concentrations
- 13.6Solvation of soluted molecules
- 13.6.1Difference between gas phase and solution properties
- 13.6.2The supermolecule approach
- 13.6.3Continuum models for describing solvation
- 13.6.4Cavitation models
- 13.6.7Monte Carlo calculations
- 13.6.8Methods of molecular dynamics
- 13.7Practical Models for intermolecular potentials
- Density Functional Theory
- Introduction to DFT
- 1.1History of DFT (Thomas-Fermi model)
- 1.2Present and future impact of DFT on Chemistry
- Properties of the exact electron density distribution
- 2.1Why to use a density-based theory?
- Hohenberg-Kohn Theorems
- 3.1Searching for the ground-state energy
- 3.2The first Hohenberg-Kohn Theorem
- 3.3The second Hohenberg-Kohn Theorem
- 3.4Spin Polarization
- 3.5Scheme for calculations based on the Hohenberg-Kohn theorems
- Kohn-Sham Equations
- 4.1Partitioning of the Hohenberg-Kohn functional F[n]
- 4.2The decomposition of the kinetic energy T[n]
- 4.3The decomposition of the potential energy V[n]
- 4.4The Kohn-Sham equations
- 4.5The adiabatic connection scheme
- 4.6Partitioning into exchange and correlation contributions
- Uniform Electron Gas: The Local Density Approximation (LDA)
- 5.1The main idea
- 5.2Exchange in LDA
- 5.3Correlation in LDA
- 5.4Advantages and disadvantages of LDA
- Gradient Corrected DFT
- 6.1Gradient expansion
- 6.2Generalized Gradient Approximation (GGA)
- 6.3Exchange in GGA
- 6.4Correlation in GGA
- Overview over Density Functionals
- 7.1Exchange Functionals (Slater exchange, Xa approximation, Becke exchange correction, Becke-Roussel)
- 7.2Correlation Functionals (VWN, Perdew-Wang, Lee-Yang-Parr)
- 7.3Hybrid methods
- Improvement of Density Functionals
- 8.1Asymptotic behavior
- 8.2Limiting cases: homogenous systems, one-electron systems
- 8.3The Becke 95 correlation functional
- 8.4Exact KS potentials and their application
- 8.5Model KS potentials
- Implementation of DFT
- 9.1Programming of the Kohn-Sham Equations
- 9.2Numerical Quadrature (Gauss quadrature schemes, accuracy)
- 9.3Use of auxiliary bases for densities and potentials
- 9.4Available DFT programs
- 9.5DFT in Gaussian94
- DFT methods with Linear scaling
- 10.1Fast multipole method
- 10.2KWIK
- 10.3Integration of functionals using PYS balls
- 10.4Use of plane waves
- 10.5Use of wavelets
- Application of DFT methods
- 11.1Basis sets for DFT
- 11.2Energy derivatives
- 11.3Energies and geometries
- 11.4Vibrational frequencies and IR intensities
- Calculation of magnetic properties with DFT methods
- 12.1Uncoupled DFT methods
- 12.2SOS-DFPT methods
- 12.3Current-DFT - An unsolved problem
- DFT and Excited States
- 13.1Hohenberg-Kohn theorems and excited states
- 13.2Approaches to treat excited states
- 13.3ROSS-DFT and MCSCF-DFT
- Transition states and van der Waals complexes
- 14.1Basic Failures when describing transition states
- 14.2Description of H bonding
- 14.3Description of van der Waals complexes
- 14.4Improvement of DFT
- DFT and Chemical Concepts
- 15.1Chemical potential and electronegativity
- 15.2Hardness and softness: HSAB concept
- 15.3Fukui function
- Mathematics for Quantum Chemists
- Vector algebra
- 1.1Scalar product
- 1.2Vector product
- 1.3Triple product
- Infinite series
- 2.1Fundamental concepts
- 2.1.1Geometrical series
- 2.1.2Harmonic series
- 2.1.3Alternating series
- 2.2Convergence criteria
- 2.2.1Cauchy criterion
- 2.2.2d'Almbert criterion
- 2.3Series expansion of functions
- 2.3.1Taylor series (MacLaurin’s series)
- 2.3.2Power series
- 2.4Complex numbers
- 2.4.1Elementary operations
- 2.4.2Euler representation
- Vector analysis
- 3.1Scalar and vector fields
- 3.2Vector calculus
- 3.2.1Curves
- 3.2.2Arclength
- 3.2.3Tangent, curvature and torsion
- 3.3Gradient, Ñ
- 3.4Divergence, Ñ•
- 3.5Curl, Ñx
- 3.6Successive application of Ñ operator, the Laplacian
- 3.7Integral relations (Gauss, Stokes)
- Coordinate systems
- 4.1Curvilinear coordinates
- 4.1.1Metric
- 4.1.2Gradient
- 4.1.3Divergence
- 4.1.4Laplacian
- 4.1.5Curl
- 4.2Rectangular Cartesian coordinates
- 4.3Circular cylindrical coordinates
- 4.4Spherical polar coordinates
- Tensors
- 5.1Linear mapping of vectors, second-rank tensors
- 5.2Basis, tensor coordinates and components
- 5.3Tensors of arbitrary rank
- 5.4Elementary operations with tensors
- 5.5Special tensor
- 5.6Principal axes and values
- 5.7Vector and tensor fields, tensor analysis
- 5.8Multipole moments, irreducible tensors
- 5.9Behavior of tensors under coordinate rotations
- Ordinary Differential Equations (ODE’s)
- 6.1General
- 6.2Order of ODE’s, explicit and implicit ODE’s
- 6.3Initial problems, several kinds of problems
- 6.4ODE’s of first order
- 6.4.1Some types of exactly solvable ODE’s
- 6.4.2Linear first-order ODE’s
- 6.4.3Existence and uniqueness of solutions, the initial-value problem for the 1st-order ODE
- 6.5ODE’s of higher order, systems of ODE’s
- 6.5.1Linear ODE of order ≥ 2
- 6.5.2Linear ODE of second order with constant coefficients
- 6.5.3Systems of linear ODE of second order with constant coefficients
- 6.5.4Initial value, boundary value, and eigenvalue problems
- 6.5.5Sturm-Liouville theory and special function systems
- 6.5.5.1Sturm-Liouville problems
- 6.5.5.2Some important systems of special functions
- Partial differential equations (PDE’s)
- 7.1Linear PDE of second order (LPDE2)
- 7.1.1The hyperbolic differential equation
- 7.1.2The parabolic differential equation
- 7.1.3The elliptic differential equation
- 7.2Some remarks on non-linear PDE’s
- 7.3Appendix A1: Spherical harmonics
- 7.4Appendix A2: Dirac’s d -function
- Variational calculus
- 8.1Functionals and functional derivatives
- 8.2Variational problems without constraints
- 8.3Variational problem with constraints
- 8.4Variational problems with local constraints
- 8.5Addendum: Ritz method for the Schrödinger equation
- Vector Spaces
- 9.1Vector Algebra: A short repetition
- 9.2Vector space
- 9.2.1Cartesian vector space R3
- 9.2.2Covariant and contravariant components of a vector
- 9.3Linear vector space
- 9.3.1Definition of linear space L
- 9.3.2Linear dependence and linear independence
- 9.4Unitary vector space
- 9.4.1Function space
- 9.5Norm of an element
- 9.6Cauchy-Schwarz Inequality
- 9.7Triangle Inequality
- 9.8Angle between two elements
- 9.9Distance between two elements
- 9.10Hilbert Space
- 9.10.1Cauchy Criterion
- 9.10.2Hilbert Space of the square-integrable functions
- 9.11Overview over Spaces
- Operators in Quantum Mechanics (DC)
- 10.1Linear Operators
- 10.2Eigenfunctions of linear operators
- 10.3Matrix elements
- 10.4Adjoint operators (Hermitian conjugate)
- 10.5Hermitian operators
- 10.5.1Properties of Hermitian Operators
- 10.5.2Examples of Hermitian operators
- 10.6Unitary operators and unitary transformations
- 10.6.1Unitary transformation
- 10.6.2Unitary transformation of an Hermitian operator
- 10.6.3The infinitesimal unitary operator
- 10.7Normal operators
- 10.8Projection operators
- 10.9Functions of operators
- 10.9.1Differentiation of an operator
- 10.10Commutator of operators
- 10.11Overview over operators used in Quantum Mechanics
- Matrices and Determinants
- 11.1Linear equation systems
- 11.2Some basic definitions
- 11.3Matrix addition and matirx multiplication
- 11.3.1Addition
- 11.3.2Multiplication
- 11.3.3Falk diagrams
- 11.3.4Commutating matrices
- 11.4Special matrices with real numbers
- 11.4.1Transposed Matrix
- 11.4.2Symmetric and anti(skew)-symmetric matrices
- 11.4.3Triangular matrix
- 11.5Determinants
- 11.6Rank of a matrix and singular matrix
- 11.7The inverse of a matrix
- 11.8Special matrices with complex numbers
- 11.8.1Complex and conjugate-complex matrices
- 11.8.2The adjoint (hermitian conjugate) matrix
- 11.8.3Hermitian and anti(skew)-Hermitian matrix
- 11.8.4Orthogonal and unitary matrices
- 11.8.5Normal matrices
- 11.9Overview over matrices
- Eigenvalue problems
- 12.1Solving linear equation systems
- 12.1.1Gauss elimination
- 12.1.2Existence and general properties of solutions
- 12.2Eigenvalue equations
- 12.3Eigenvalues of Hermitian and other matrices
- 12.3.1Similarity transformations and Invariants
- 12.3.2Invariants of an unitary transformation
- 12.3.3Estimates of the eigenvalues of Hermitian matrices
- 12.3.4The Raleigh quotient
- 12.4Eigenvalues of a complex matrix
- 12.5Diagonalization of matrices
- 12.5.1Jacobi diagonalization
- 12.5.1.1Algorithm for a Jacobi diagonalization
- 12.5.2Givens-Householder diagonalization
- 12.5.2.1Givens diagonalization
- 12.5.2.2Householder diagonalization
- 12.5.3Diagonalization of large matrices
- 12.5.4Lanczos method
- 12.5.5Nesbet method (see CI course)
- 12.5.6Davidson method (see CI course)
- 12.6Quadratic forms
- 12.6.1Differentiation of a quadratic form
- 12.6.2Definiteness of matrices
- 12.6.3Characterization of rectangular matrices
- 12.6.4Diagonalization of rectangular matrices
- 12.7Matrix Factorization
- 12.7.1LU Factorization and the Gaussian Elimination revisited
- 12.7.2The LDLT and Cholesky factorizations
- 12.7.3QR and QL (LQ) factorizations
- 12.7.4Spectral decomposition of a matrix
- 12.8A non-unit metric: Orthogonalization procedures
- 12.8.1Gram-Schmidt Orthonormalization
- 12.8.2Löwdin procedures
- 12.8.2.1Symmetric orthonormalization
- 12.8.2.2Canonical orthonormalization
- 12.8.3Comparison and application of orthonormalization procedures
- 12.9Overview over eigenvalue problems
- Optimization
- 13.1Definition of optimization problems
- 13.2Elements of multivariate analysis
- 13.2.1Continuity
- 13.2.2Differentiability, gradient, hessian
- 13.2.3Taylor’s theorem
- 13.2.3.1Finite difference approximations to derivatives
- 13.2.4Contour plots
- 13.3Stationary points of multivariate functions
- 13.3.1Minima, global and local
- 13.3.2Local versus global methods
- 13.3.3Convergence characterization
- 13.4Optimization methods used in Quantum Chemistry
- 13.4.1Energy-only methods
- 13.4.1.1Univariate search
- 13.4.1.2Simplex method
- 13.4.2Gradient methods
- 13.4.2.1Steepest descent methods
- 13.4.2.2Conjugate gradient methods
- 13.4.2.3Nonlinear conjugate gradient methods
- 13.4.3Newton methods
- 13.4.3.1Discrete Newton
- 13.4.3.2Quasi Newton methods
- 13.4.3.3Rank 1 methods, (Broyden’s method)
- 13.4.3.4Rank 2 methods
- Probability and Statistics
- 14.1Probability, definitions and theorems, Venn diagrams
- 14.1.1Counting sample points
- 14.1.2Probability of an event
- 14.1.2.1Additive rules
- 14.1.2.2Multiplicative rules
- 14.1.2.3Bayes’ rule
- 14.2Random variables and probability distributions
- 14.2.1Discrete probability distributions
- 14.2.2Continuous probability distributions
- 14.2.3Empirical distributions
- 14.2.3.1Stem and leaf plot
- 14.2.3.2Frequency distribution
- 14.2.4Joint probability distributions
- 14.2.4.1Marginal distributions
- 14.2.4.2Conditional probability distributions
- 14.2.4.3Statistical independence
- 14.3Mathematical expectation
- 14.3.1Mean of a random variable
- 14.3.2Variance and covariance, standard derivation
- 14.3.3Correlation coefficient
- 14.3.4Chebyshev’s theorm
- 14.4Some discrete probability distributions
- 14.4.1Discrete uniform distribution
- 14.4.2Binomial and multinomial distributions
- 14.4.2.1The Bernulli Process
- 14.4.3Hypergeometric distribution
- 14.4.4Poisson distribution and the Poisson process
- 14.5Some continuous probability distributions
- 14.5.1Continuous uniform distribution
- 14.5.2Normal distribution
- 14.5.3Areas under the normal curve
- 14.5.4Normal approximation to the binomial
- 14.5.5Gamma and exponential distributions
- 14.5.6Relationship between Gamma, exponential and Poisson distribution
- 14.5.7Other continuous distributions
- 14.5.7.1Chi-square distribution
- 14.5.7.2Logonormal distribution
- 14.5.7.3Weibull distribution
- 14.6Fundamental sampling distributions
- 14.6.1Central tendency in the sample
- 14.6.2Variability in the sample
- 14.6.3T-distribution
- 14.6.4F-distribution
- Catastrophe Theory
- 15.1The cusp catastrophe
- 15.2The dynamic that causes catastrophes
- 15.3The mechanism of aggression
- 15.4Divergence
- 15.5Thom’s classification theorem
- 15.6Thom’s seven elementary catastrophes
- 15.7The butterfly catastrophe
- 15.8Structural changes and molecular graphs
- 15.9Description of reaction mechanism: H
_{2}+ O(^{3}P) - Presentation Techniques in Chemistry – How to write a paper? How to give a seminar?
- Scientific Research and Scientific Writing
- 1.1The ultimate result of scientific research is publication
- 1.2Scientific communication is a 2-way process
- 1.3Thinking and Writing
- 1.4There is a well-defined path from thinking to writing
- 1.5From thinking to writing in TC
- 1.6List of questions to be answered before writing
- What is a “Scientific Paper”
- 2.1Types of scientific communications
- 2.2Definition of a scientific paper: primary publication
- 2.3Organization of a scientific paper
- 2.4Drafting a scientific paper
- 2.4.1The writing process
- 2.4.2Transitions
- 2.4.3The Role of tangible details
- 2.4.4Keeping the speed of writing.
- 2.5Perception of a paper
- 2.6Order of writing up the paper
- 2.7Preparing the actual write-up: Notes for authors
- The various parts of a Journal Article
- 3.1The Result part
- 3.2The Method part
- 3.3The Discussion part
- 3.4The Introduction part
- 3.5The Conclusion
- 3.6The Abstract
- 3.7The Title
- 3.8Authors
- 3.9Acknowledgement
- 3.10References
- 3.11Supporting Information
- 3.12Appendix
- General Rules and Use of Language
- 4.1Basic rules
- 4.2Scientific language
- 4.3Choice of the correct word or phrase
- 4.4Articles
- 4.5Comparisons
- 4.6Parallelism

The course is structured into five parts:

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

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.

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.

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?

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.

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.

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.

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.

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.

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.

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.

M^{4}-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

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

Model space and orthogonal space, projection operators.

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