KE522: Quantum Chemistry and Theoretical Spectroscopy (10 ECTS)

STADS: 10012901

Level
Bachelor course

Teaching period
The course begins in the autumn semester and continues in the spring semester.

Teacher responsible
Email: hjj@sdu.dk

Additional teachers
kongsted@sdu.dk

Timetable
Show entire timetable
Show personal time table for this course.

Comment:
Samlæses med KE818 uge 36-46.

Prerequisites:
None.

Academic preconditions:
Students taking the course are expected to:

• Have knowledge of the content of the mathematics, physics and chemistry parts of the first year courses in the bachelor degree program.
• If KE529 or similar courses are not known, extra study time will be needed for the necessary mathematics in the course.
• Be able to use the mathematical tools from first year incl. KE529, as well as classical physics (especially kinetic and potential energy, momentum and angular momentum, forces, Coulomb potential).

Course introduction
The aim of the course is to provide the students with a basal theoretical understanding of molecular electronic structure, chemical bonding and reactivity, as well as optical spectroscopy based on the quantum mechanical description of atoms and molecules. This includes group theory and its consequences for the electronic structure and optical spectra of molecules.

The course builds on the knowledge acquired in all first-year courses in the bachelor program in chemistry and the second year course.

The course gives an academic basis for studying the topics NMR and other spectroscopies, inorganic ligand-field theory etc., physical organic chemistry,  molecular modelling, computational quantum chemistry, as well as ISA’s and bachelor project in theoretical chemist. These topics are or may be part of the bachelor and master degrees.

In relation to the competence profile of the degree it is the explicit focus of the course to:

• Give the competence to interpret electronic, vibrational and rotational properties of molecules based on quantum mechanics, with special focus on molecular orbital theory
• Give skills to use quantum chemistry computer programs for modelling of molecules on an introductory level
• Give knowledge and understanding of molecular orbital theory and the underlying quantum mechanics as well as the theoretical basis for rotational, vibrational and electronic spectroscopy.

Expected learning outcome
The learning objectives of the course is that the student demonstrates the ability to:

• account for the quantum chemical principles and the necessary mathematical techniques, especially the superposition principle and the variation principle.
• explain the solution of the Schrödinger equation for a particle in a box and tunnelling for a rectangular barrier
• write the electronic and total Hamiltonian operators for any molecule and explain the meaning of each part.
• account for and use the Born-Oppenheimer approximation, the Pauli principle, Hund’s rules, the variation principle, the superposition principle.
• account for the quantum mechanical description of angular momentum and its significance for the description of molecular rotational spectra and the angular momentum of electrons in atoms and linear molecules.
• account for spin, fermions and bosons, coupling of spin with spin and coupling of spin with orbital angular momentum (spin-orbit).
• account for the solutions to the Schrödinger equation for one-electron atoms and be able to couple the spin and angular momentum of atomic orbitals correctly to give the total values for many-electron systems, including writing of term symbols for atoms.
• use the concept of shielding (screening) to explain the properties of atoms in molecules: electronegativity, ground state of transition metals, trends in ionisation energies and electron affinities, differences in binding properties for different oxidation states.
• determine symmetry elements, symmetry operations, and point groups; and classify molecules with respect to point group and rotor type
• use group theory for chemical problems, including:
• evaluate if a molecule is polar and chiral
• determine irreducible representations for functions and products of these
• determine if a volume integral over products of symmetry functions is zero because of symmetry
• construct symmetry orbitals from a set of atomic orbitals
• construct symmetry coordinates from a set of atomic coordinates
• determine the symmetry of a Slater determinant from the symmetries of its occupied orbitals
• which orbitals can interact and which many-electron wave functions (in particular Slater determinants) can interact
• write down electron configurations and term symbols for molecules
• determine if a given optical transition between two quantum states (absorption or emission) is dipole allowed or forbidden.
• predict electronic spectra, photo electronic spectra, vibrational spectra, rotational spectra and combinations (UV/vis, Xray, PES, XPS, IR, Raman, MW)  and combinations for all types of molecules  based on molecular symmetry and dipole selection rules, including:
• determine the distribution of the normal vibrations on symmetry species
• predict if a given normal vibration might be observed in IR and Raman spectra based on its symmetry
• account for the quantum mechanical description of a harmonic oscillator and explain how it can be used to interpret IR and Raman vibrational spectra as well as vibrational structure in electronic spectra by means of Frack-Condon factors
• account for spin-orbit coupling and its importance for optical spectra, in particular phosphorescence
• perform molecular orbital calculations with the quantum chemistry program system used at the computer exercises and interpret the results of the calculations
• use the relevant competences stated above to undertake a quantum chemistry project that extends the textbook material in the course, and explain, interpret and put into perspective the results of the project at the oral exam.

Emphasis is placed upon the familiarity of the student with the concepts related to the major topics of the course, and ability to combine different concepts to address more complex problems.

Subject overview
The following main topics are contained in the course:

• Schrödinger equation and quantum mechanical principles
• atomic orbitals, shielding and atomic orbital energies
• Born-Oppenheimer approximation
• molecular orbitals and electronic states
• group theory for point groups, character tables and their uses for determination of symmetry-adapted functions and spectroscopic selection rules (IR, Raman, UV/vis)
• variation principle and introduction to perturbation theory
• introduction to computational quantum chemistry and evaluation of results
• introduction to time-dependent perturbations and the interaction between light and matter
• introduction to theoretical description of chemical reactions
• theoretical background for optical rotational, vibrational, electronic, and photoelectron spectroscopy

Literature

• Atkins, de Paula & Friedman: Physical Chemistry: Quanta, Matter, and Change 2e, ISBN 9780199609819.
  BEMÆRK: det er IKKE den samme "Atkins Physical Chemistry" som bruges i fysisk kemi kurset!

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam

1. Mandatory assignment in the spring semester is a prerequisite for taking part in exam b). Pass/fail, internal marking by teacher. (10012912).

Assessment and marking:

1. Autumn semester: Two mandatory assignments and an electronic test. Overall assessment on a pass/fail basis, internal marking by teacher. (5 ECTS). (10012802).
2. Spring semester: A 30 minutes oral examination in June. The examination is partly a defence of the prerequisite assignment, partly a question from the syllabus. Overall assessment, graded by the Danish 7-mark scale and external examiner. (5 ECTS). (10012902).

Expected working hours
The teaching method is based on three phase model.
Intro phase: 50 hours
Skills training phase: 50 hours, hereof:
 - Tutorials: 40 hours
 - Laboratory exercises: 10 hours

Educational activities Study phase: 130 hours

Activities during the study phase:

• 50 hours reading of text book and lecture notes
• 20 hours preparation for tutorials
• 15 hours for 2 home assignments and electronic test
• 20 hours for project work
• 25 hours for exam preparation

Educational form
The teaching in the so-called intro lessons will be a mixture of teacher and student centered learning, where the students solve activating problems going deeper into what the teacher just has introduced.

Language
This course is taught in English, if international students participate. Otherwise the course is taught in Danish.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.