Quantum Mechanics of Molecular Systems

Schrödinger equation and wavefunctions

particle in a box
harmonic oscillator
anharmonic corrections
rigid rotor

molecular states

Born-Oppenheimer approximation

Slater-determinants
electron structure calculations for molecular systems (LCAO-MO)

electron-vibration coupling

transitions between states,

semiclassical curve crossing

Landau-Zener model

time dependent perturbation theory

Fermi's golden rule
optical transitions

After participating, the students are able to apply simple quantum mechanical models to molecular systems to analyse molecular states and transitions.

They are able

-  to describe Pi-electron systems of molecules with conjugated double bonds within the free electron model

- to formulate the Hamiltonian of a harmonic oscillator with ladder operators and to solve the time independent Schrödinger equation

- describe anharmonic effects with perturbation theory

- determine localized wave packets which solve the time dependent Schrödinger equation for free particles and particles in a harmonic potential

- to formulate the Hamiltonian of a molecular system and to apply the Born-Oppenheimer approximation to separate the motion of electrons and nuclei

- to describe the ground state of a many electron system with a Slater determinant

- to describe modern electron structure methods

- to apply the quasiclassical approximation to molecular transitions and to derive the Landau Zener rate expression with perturbation theory

- to derive the rate expression for molecular transitions into a continuum of final states and to apply it to optical transitions

- to interpret optical spectra of larger molecules on the basis of electron-vibration coupling

basic quantum mechanics

lecture-style mediation of knowledge

interactive applets visualizing functional dependencies (individual sudies)

extra materials for more details (individual studies)

blackboard

laptop/projector

lecture notes

Java applets

extra material (additional notes)

P.O.J. Scherer, S.F. Fischer Theoretical Molecular Biophysics

Haken, Wolf Molekülphysik und Quantenchemie

Schwabl, quantum mechanics

lecture notes

There will be an oral exam of 25 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

• to describe Pi-electron systems of molecules with conjugated double bonds within the free electron model
• formulate the Hamiltonian of a harmonic oscillator with ladder operators and to solve the time independent Schrödinger equation
• describe anharmonic effects with perturbation theory
• determine localized wave packets which solve the time dependent Schrödinger equation for free particles and particles in a harmonic potential
• formulate the Hamiltonian of a molecular system and to apply the Born-Oppenheimer approximation
• describe the ground state wavefunction of a many electron system
• describe modern electron structure methods
• apply the semiclassical approximation to molecular transitions and derive the Landau Zener rate expression with perturbation theory
• derive the rate expression for molecular transitions into a continuum of final states and apply it to optical transitions
• interpret optical spectra of larger molecules on the basis of electron-vibration coupling