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### Vår 2021

# KJE-2001 Molecular physical chemistry and foundations of spectroscopy - 10 stp

## The course is administrated by

Institutt for kjemi

## Type of course

Theoretical course. The course is available as a singular or elective course independent of study program, also to exchange students. The course is offered on condition that a minimum number of students register for the course.

## Course overlap

K-210 Theoretical chemistry 10 stp

## Course contents

Atoms and molecules are the tiniest building blocks of anything that surrounds us. They are so small that they challenge the physics which we are used to. Indeed they no longer abide to Newton's laws but they behave according to the laws of Quantum Mechanics. This is challenging as Quantum Mechanics clashes with our common sense, but also fascinating, making it possible to reveal and exploit the unique properties of atoms and molecules: the technological world we are used to, with powerful computers in the palm of our hands (a modern smartphone could have easily made it to the top-100 supercomputer list 20 years ago!) heavily relies on the quantic properties of matter for the construction of the necessary components. Investigating atoms and molecules is challenging: to "measure" them we need to make use of even smaller particles: photons. The interaction of matter with photons give rise to a wide range of spectroscopic methods which are among a chemist's finest tools. Some spectroscopic techniques such as infrared spectroscopy are now routinely performed in any chemistry lab. Others such as Magnetic Resonance are not only a powerful investigation method of molecular structure but have extended far beyond chemistry to biology and medicine. In the present course the foundation of Quantum Mechanics will be presented: after a historical introduction (discovery of quanta, black-body radiation, electron diffraction, photoelectric effect) the postulates of quantum mechanics and their interpretation will be presented. We will then connect them to some simple exact models (harmonic oscillator, particle on a sphere, hydrogenionic systems) emphasizing the aspects connected to atomic and molecular structure. We will then turn our attention to the electronic structure of atoms and molecules. The simplest electronic structure models and tools (atomic orbitals and electron correlation, LCAO, molecular orbitals, Hückel’s model) will be semi-quantitatively presented. The link from the molecular level to the macroscopic world, statistical mechanics shall be introduced: a macroscopic system is a large collection of molecules which must obey strict statistical laws, providing a sound molecular interpretation for classical thermodynamics. We will finally focus on spectroscopic techniques. We will describe how molecules interact with light (photons) at different frequency giving rise to a variety of methods addressing important questions about molecular structure: such as bond lengths and strengths, connectivity, electronic states, intermolecular interactions. Among the techniques that will be presented are Rotational spectroscopy, Vibrational spectroscopy, Electronic spectroscopy, Raman techniques, Nuclear Magnetic Resonance, Electron Spin Resonance. The first three will be discussed in detail, whereas the other three will only briefly touched upon. Spectroscopic techniques are a vast subject: by no means the present course could cover all of them. Students are therefore encouraged to put forward specific techniques they wish to learn about so that they could be covered during the course, at least in their general aspects.

## Application deadline

Applicants from Nordic countries: 1st of June for the autumn semester and 1st of December for the spring semester. Applicants from outside the Nordic countries: 1st of October for the spring semester and 15th of April for the autumn semester.

## Admission requirements

Required:

- Basic physical chemistry (i.e KJE-1005 or equivalent)
- Basic knowledge in calculus (i.e. either MAT-0001 or MAT-1001)

Recommended:

- Basic knowledge in physics (elementary classical mechanics and electromagnetism)
- Calculus 2 and elementary linear algebra (i.e MAT-1002 and MAT-1004 or equivalent)

Søknadskode 9336 enkeltemner i realfag.

## Objective of the course

The student will have expanded proficiency within relevant topics in chemistry. This means that the student

Knowledge

- can use the postulates of quantum mechanics to solve exactly the simplest systems: particle in a box, particle on a circle
- can explain the features of such models in light of their respective wavefunction
- can analyze more advanced solvable models (particle on a sphere, harmonic oscillator, hydrogen atom) through the knowledge of the easier ones (box, circle)
- can explain the features of atomic and molecular systems in light of the knowledge acquired about solvable models
- can explain the Boltzmann distribution and the partition function
- can describe the main general features of spectroscopic methods to investigate the molecular structure
- can use the acquired fundamental knowledge to interpret simple rotational, vibrational and vibrational-rotational spectra
- can describe the main features of electronic spectra and the underlying dynamics of the excited states
- can identify and describe the fundamental features and underlying principles of more advanced spectroscopic techniques: Raman spectroscopy (vibrational and rotational), Magnetic spectroscopy (NMR, EPR)

Skills

- can solve simple problems for the model systems (particle in a box, particle on a circle/sphere, harmonic oscillator, hydrogen atom)
- can explain atomic properties/structure and spectroscopy in light of the principles of quantum mechanics and the solvable models
- can relate the main features of molecular spectroscopy (e.g. band structure, band intensity, shape, energy range) to the acquired knowledge of quantum mechanics
- can explain the details of simple molecular spectra and relate them to the molecular structure (e.g. bond length and strength, connectivity, electronic structure)
- can explain and make use of the Hückel model to explain the electronic structure of conjugated compounds, with particular reference to the concept of aromaticity
- can make use of statistical mechanics to explain observable phenomena such as features of molecular spectra, heat capacities, phase transitions

Competence

- can explain the main traits of quantum mechanics and the main differences with respect to classical mechanics
- can use quantum mechanics arguments to describe the structure of atoms and molecules
- can analyze the main features of atomic and molecular spectra, relating them to the molecular structure and to the underlying laws of quantum mechanics
- can connect molecular structure to thermodynamic quantities (free energy, heat capacity) through statistical mechanics and the molecular partition functions

## Language of instruction

The language of instruction is English and all syllabus material is in English.

## Teaching methods

Lectures: 30 h

Seminars: 30 h

## Assessment

A final oral exam at the end of the course (duration approximately 50 min). Letter grades A-E, F - fail.

Coursework requirements: Three approved assignments.

Examination questions will be given in English or Norwegian, and may be answered either in English or Norwegian/a Scandinavian language.

Students who have not passed the last ordinary exam may re-sit the oral exam the following semester.