ESQC lectures
Except for autodidactic purposes,
you are not allowed to use these notes without written consent from the authors.
Jürgen Gauss (Mainz)
Coupled Cluster Theory
(3 lectures)
[
pdf 1/2
pdf 2/2
]
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.
Trygve Helgaker (Oslo)
Molecular properties
(4 lectures)
[
pdf 1/3
pdf 2/3
pdf 3/3
]
The analytical calculation of molecular properties with emphasis on first- and
second-order properties. Variational Lagrangian for non-variational
electronic-structure models. The 2n+1 and 2n+2 rules. Molecular gradients and
molecular Hessians. Molecular structure and vibrational frequencies. The
electronic Hamiltonian in an electromagnetic field. Gauge dependence and London
orbitals. NMR shielding and indirect nuclear spin-spin coupling constants.
Geometry optimizations. Newton and quasi-Newton methods. Minima and saddle
points.
Wim Klopper (Karlsruhe)
Basis Sets, Integrals and SCF Methods
(4 lectures)
[
pdf 1/4
pdf 2/4
pdf 3/4
pdf 4/4
]
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.
Per-Åke Malmqvist (Lund)
Mathematical Tools in Quantum Chemistry
(2 lectures)
[
pdf 1/4
pdf 2/4
pdf 3/4
pdf 4/4
]
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.
Benedetta Mennucci (Pisa)
Hybrid QM/classical models in Chemistry
(2 lectures)
[
pdf 1/2
pdf 2/2
]
Introduction to the modeling of solvent effects. Atomistic versus continuum
approaches. Hybrid quantum mechanical- classical solvation models. Effective
Hamiltonians and self consistent reaction field. The coupling of solvent
effects and electronic correlation. Solvent effects on molecular properties and
spectroscopies. Bulk versus specific solvation. Formation and relaxation of
excited states of solvated systems. Nonequilibrium and solvatochromism.
Frank Neese (Mülheim)
Algorithm design
(1 lecture)
[
pdf 1/1
]
Efficient implementation of quantum chemical equations. Do's and don'ts of quantum chemical programming. Obtaining exact numbers in the most efficient way vs. obtaining approximate numbers efficiently
Approximation methods
(1 lecture)
[
pdf 1/1
]
The lecture will cover a range of approximation methods that are in widespread use in quantum chemistry and will discuss their advantages and disadvantages. Special attention will be given to numerical thresholding and controlled precision. Applications to the self-consistent field (Hartree-Fock & DFT) as well as MP2 will be briefly touched upon.
Local correlation
(1 lecture)
[
pdf 1/1
]
Various approaches to calculating the dynamic correlation energy for large molecules: incremental methods, domain based local schemes, pair natural orbital approaches
General aspects of computational chemistry
(1 lecture)
Design issues encountered in planning an actual computational chemistry study. Incentive for thinking about the goals of the computational study, but not a set of 'carved in stone' recipes. Actual example
Jeppe Olsen (Aarhus)
The Multiconfigurational Approach
(3 lectures)
[
pdf 1/1
]
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.
Introduction to Response Theory
(1 lecture)
[
pdf 1/1
]
This lecture gives a short introduction to response functions and their use to
describe the properties of ground and excited states. The response functions
are introduced as terms in the expansion of the the time-development of an
expectation value for a Hamiltonian including a time-dependent perturbation. It
is shown that the linear response function provides information about
excitation energies and transition moments. The quasi-energy is introduced and
the equality between the stationarity of this energy and the time-dependent
Schrödinger equation is discussed, which allows the use of the
quasi-energy to obtain the time-development for approximate wave functions and
densities. A brief overview of the various approximate response models is
given, including their computational complexity and limitations.
Trond Saue (Toulouse)
Second Quantization
(2 lectures)
[
pdf 1/2
pdf 2/2
]
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.
Case study: the case of orbitals
(1 lecture)
[
pdf 1/1
]
Ths lectures stresses the difference between spectroscopic and chemical orbitals.
David Tozer (Durham)
Density Functional Theory
(3 lectures)
[
pdf 1/1
]
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.
Lucas Visscher (Amsterdam)
Relativistic Quantum Chemistry
(3 lectures)
[
pdf 1/1
]
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. Effective Core Potentials. Spin-orbit coupling in
molecules. Applications of relativistic methods in heavy-element chemistry.
Peter Taylor (Tianjin)
Case study: all molecules are the same !
(1 lecture)
[
pdf 1/1
]
It is established mathematically that for sufficiently large total nuclear charge Z and as the internuclear distance decreases towards zero, all neutral diatomic molecules have the same leading term for the exact energy (in a scaled unit system), and that this is the Thomas-Fermi energy. Further, the Hartree-Fock energy shows exactly the same behaviour. Given that the Born-Oppenheimer Hamiltonian for a diatomic molecule already contains examples of all interaction terms that would appear in the polyatomic case, the diatomic result is a general molecular observation. Further, it holds if relativity is concerned. So in this sense all molecules are the same!
Unfortunately, the mathematics does not provide quantitative information on "sufficiently large Z", nor on "distance decreases towards zero". We have therefore investigated the matter computationally. The results may surprise you...