554017 Advanced Computational Chemistry
(Laskennallisen kemian jatkokurssi)
addresses the methods used in ab initio molecular electronic-structure
theory. Its focus is at wave-function-based methods and their origin in
fundamental quantum mechanics.
The course covers the following topics:
- Exact and approximate many-electron wave functions and their
- One-electron basis sets
- Molecular integral evaluation
- Second quantization formalism
- Solution of the Hartree-Fock equations
- Configuration interaction, coupled-cluster and perturbation
- Numerical benchmarking and calibration of the considered
The course is targeted at graduate or advanced undergraduate
students in chemistry or physics with preliminary knowledge of quantum
mechanics and an interest in working in the fields of computational and
theoretical chemistry. Participants who are already familiar with
quantum chemistry will deepen their knowledge on the fundamental basis
of the commonly used methods, while students of other disciplines can
get hands-on experience on the methods for solving the Schrödinger
equation in the case of many interacting particles.
- Credits: 4 ECTS. Successful examination or a project work as
well as a couple of obligatory exercises are required for the credits.
- Lecturer: Dr. Pekka Manninen, docent (email:
pekka.manninen(at)csc.fi), tel. +358-50-3819039.
- Language: English if necessary; otherwise Finnish.
- Lectures: Mondays 3.30 pm to 5 pm; 30 hours in total. First
lecture Jan 12 2009. Room A120 (Chemicum building, Kumpula campus).
- Literature: Selected parts of T. Helgaker, P.
Jørgensen, and J. Olsen, Molecular Electronic-Structure Theory
- Prerequisities: Either of the courses Introduction to
computational chemistry (Johdatus laskennalliseen kemiaan) or
Computational chemistry (Laskennallinen kemia) is recommended, but one
or more courses in basic quantum mechanics and/or quantum chemistry is
Lecture notes (pdf)
(1.1 MB) for the course. Last update Jan 11 2009.
Examples of project work topics
The following are suggestions for project works. Feel free
to suggest modifications into them or a topic that interests
you more and/or fits to your current research.
Correlation-consistent basis sets In this project, you
will acquaint yourself with the correlation-consistent basis sets,
which are the most "physical" Gaussian basis sets in the literature,
Discussion in terms of basis-set completeness suits naturally
- a survey of the underlying ideas
- the basis-set convergence in Hartree--Fock calculations on
some small molecules for the electronic energy and
geometrical parameters using the correlation-consistent
hierarchy; as well as the correlation energy obtained
by the MP2 and/or CCSD level of theory
- address the core-polarization and augmentation of the
Configuration state functions
As discussed in the lectures, the exact non-relativistic wave
function is an eigenfunction of the total and projected spins,
whereas the Slater determinants are eigenfunctions of the
projected spin only. We can set up a basis of functions that
are simultaneous eigenfunctions of the orbital occupation-number
operators as well as the operators for the projected and total
spins - such spin-adapted functions are called configuration
state functions (CSF).
- Consider the concept and properties of CSFs
- Present the construction of CSFs using the sc.
genealogical coupling scheme
- Consider the transformations between determinant and CSF bases.
- Discuss the concept and the meaning of the size-extensivity in
many-electron wave functions
- Consider the size-extensivity in exact wave functions as well as in
approximate wave functions constructed by linear and exponential
- Give numerical examples on the issue.
Basis-set superposition error: In this project, you will
familiarize yourself with a feature of finite basis sets not discussed
on the lectures: the basis-set superposition error.
- Present the general concepts connected to the BSSE
- Discuss the
- Include numerical estimates and discussion
on BSSE in some rare-gas dimer.
- Derive the explicit form of the CC2 amplitude equations for
a closed-shell case
- Demonstrate the performance of the CC2 model in
of a few small molecules and compare them with experimental
results as well as other standard models. Remember to address
the basis-set convergence too.
- Total electronic energies
- Bond distances and bond angles
- Molecular dipole moments
Operation CCSD overload
- derive the explicit (i.e. "implementation-ready") forms for
the closed-shell CCSD wave function using the T1-transformed
- carry out a highly detailed examination of the molecular
energy of some small molecule (e.g., water or hydrogen fluoride)
- the basis-set convergence
- the composition of the total energy.
Treatment of O3 with multi-configurational wave functions
- Present the theory behind the CASSCF and CASPT models
- Build up a hierarchy of CASSCF wave functions for the
ozone molecule and compare the obtained molecular geometry
with the experimental results. Address the basis-set issues
- Apply the CASPT2 theory to refine the description of
Møller-Plesset perturbation theory
You may include some calculations for demonstration purposes.
- Present the general theory behind the Møller-Plesset theory
- Give the explicit forms of the MP1 and MP2 wave functions and
the MP2 and MP3 energy expressions
- Discuss the size-extensivity of MPPT
- Specialize the treatment to the closed-shell case
- Discuss the convergence in perturbation theory.
A detailed and well-written report (in English or Finnish)
is expected together with a short presentation at the end of the
course. The projects may be carried out in groups of two or three,
but of course doing them solely is possible too.