ESQC-09 Lectures
Second Quantization (Jeppe Olsen) - 2 lectures
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 lectures
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 (Wim Klopper) - 4
lectures
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 Multiconfigurational Approach (Peter Taylor) - 3 lectures
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 (David Tozer) - 3 lectures
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 (Jürgen Gauss) - 3 lectures
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 lectures
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 (Lucas Visscher)
- 3 lectures
Synopsis:Basics of relativistic effects in the electronic structure of
atoms
and molecules. Relativistic theory of many-electron systems. Dirac
equation
and Dirac-Coulomb-Breit equation. Transformations of the Dirac equation
to
two-component form. Douglas-Kroll transformation. Recent Applications
of the
Douglas-Kroll-transformed Hamiltonian. Effective Core Potentials.
Spin-orbit
coupling in molecules.
Accurate Calculations and Calibration (Peter Taylor) - 2 lectures
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 (Michael Robb) - 2 lectures
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 (Maurizio Cossi) - 1 lecture
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 circular dicroism, EPR and NMR
parameters. The last part concerns the two most important dynamical
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.
Tutorials/Exercises
Tutorial Leader: | Trond Saue |
Tutors: | Valera Veryazov |
Per-Olof Widmark |