ESQC-00 Lectures

Second Quantization (Jeppe Olsen) - 2 lctrs
Synopsis: The formalism of second quantization provides an alternative representation of quantum mechanics, that is useful for orbital based models. In second quantization Slater determinants are represented by occupation number vectors in an abstract vector space, the Fock space. Operators are represented by linear combinations of products of creation and annihilation operators. The use of finite basis sets leads to deviations from the usual commutators between operators.

Mathematical Tools in Quantum Chemistry (Per-Åke Malmqvist) - 2 lctrs
Synopsis: This course gives an introduction/refresher in basic nomenclature and definitions of spaces and operators of importance in quantum chemistry, and their properties. Convergence/divergence of series and of iterative processes is analyzed. Modern methods for eigenvalue problems are described, in particular for CI applications where dimensions can be very large. Similarly, solution methods for large linear and non-linear equation systems are presented.
 

Basis Sets, Integrals and SCF Methods (Reinhart Ahlrichs) - 4 lctrs
Synopsis: Basic tools and techniques of rigorous molecular electronic structure theory, fundamental for the treatment of molecular properties. The electronic Schrödinger equation. Slater determinants and the Hartree-Fock or self-consistent field (SCF) approximation. The concepts of closed and open shell states, molecular orbitals (MOs) and spin orbitals, restricted and unrestricted SCF procedures, Koopmans' and Brillouin's theorem. Introduction of a basis set (LCAO) expansion for the MOs and the Roothaan-Hall equations. Techniques for the evaluation of integrals over Gaussian functions and direct SCF procedures. Discussions of recent developments.

The Multi-Configurational Approach (Björn Roos) - 4 lctrs
Synopsis: Near degeneracies in molecular systems: transition states in chemical reactions, excited states, molecules with competing valence structures.  The MCSCF wave function and energy expression. The multiconfigurational SCF equations. The Newton-Raphson and super-CI methods. Complete and restricted active spaces. Different types of MCSCF wave functions. Excited states and transition properties. Multiconfigurational second order perturbation theory. Multireference Configuration Interaction techniques.

Density Functional Theory (Nicholas Handy) - 3 lctrs
Synopsis: Density Functional Theory. The Hohenberg-Kohn Theorem. The Kohn-Sham equations. The Exchange-Correlation Functional and the Exchange-Correlation Potential. Gradient Theory for DFT. The Local Density Functional and more sophisticated functionals involving the density gradient. Ab Initio Functionals. DFT for Excited States.

Coupled Cluster Theory (Peter Taylor) - 3 lctrs
Synopsis: Single reference correlation treatments. Size-extensivity and correct scaling of the correlation energy; qualitative form of the wave function. The exponential formulation; connected and disconnected terms. The SDCI and CCSD models; relation to perturbation theory. Higher excitations; iterative and non-iterative methods. Extensions to
open-shell systems. Approximate coupled cluster methods and their relatives.

Energy derivatives and Geometry Optimization (Trygve Helgaker) - 4 lctrs
Synopsis: Analytical calculation of ab initio energy derivatives (in particular gradients and Hessians). Variational and non-variational wave functions. Energy derivatives as a tool in quantum chemistry with emphasis on geometry optimizations. Standard methods for minimizations are described as well as transition state optimizations. Finally calculations of vibrational frequencies and reaction paths are briefly discussed.

Relativistic Effects and Effective Core Potentials (Ulf Wahlgren) - 2 lctrs
Synopsis: The Dirac equation and various  transformations to two-component form. Emphasis will be put on the Douglas-Kroll transformation which yields variationally stable equations. The Breit-Pauli equation and the no-pair equation for the spin-orbit interactions will be discussed and compared. The basic theory for effective core potentials will be discussed. Special emphasis will be given to ECP:s of the Huzinaga form with explicit core projection operators. Both traditional ECP:s and the parameter-free form suggested by Huzinaga, Seijo and Barandarian will be described. The problem of relativistic effects in conjunction with ECP:s will also be addressed.

Accurate Calculations and Calibration (Peter Taylor) - 2 lctrs
Synopsis: Uncertainties in quantum chemical calculations. Full CI (FCI) wave functions and calibrations. The one-particle expansion problem, basis sets. Examples using FCI calibrations. Other calibration approaches. Selected problems: electric field response; vibrations of alkaline-earth clusters; accurate binding energies.

Quantum Chemistry at work (Per Siegbahn) - 2 lctrs
Synopsis: Quantum chemical applications on realistic chemical problems. Applications on medium size to large systems.  Spectroscopy and chemical reactivity. Choice of chemical and computational models. Density functional theory and ab initio quantum chemical methods. Geometry optimizations. Solvent effects. Relativistic effects. Basis set effects. First and second row systems. Transition metal complexes. Quantum chemical models for catalysis, in biochemistry, and for metal surfaces.

Chemistry in condensed phases (Vincenzo Barone) - 1 lctr
Synopsis: This lecture presents some aspects of solute focused solvent models in their basic formulation. The first part analyzes electrostatic and non-electrostatic contributions at equilibrium together with their analytical firstand second derivatives. The second part is devoted to equilibrium molecularobservables including dipole (hyper)polarizabilities, vibrational circulardicroism, EPR and NMR parameters. The last part concerns the two most importantdynamical processes in condensed phase chemistry: absorption of electromagneticradiation and chemical reactions. Both these problems require explicit consideration of non equilibrium situations tuned by the speed of the solvent response to a perturbation.