Elementary Processes in Molecular Systems

• Different types of elementary processes in molecular systems
• Application of Fermi's Golden Rule to molecular transitions
• Correlation-function formalism for the rate expression
• Dephasing and lineshape
• Reorganization and Electron-Phonon coupling
• Intramolecular transitions:
• radiative (absorption, fluorescence)
• radiationless (internal conversion, intersystem crossing)
• Coherent electronic excitations (molecular aggregates, polymers)
• Incoherent energy transfer (Förster-transfer and Dexter mechanism,  disorder and narrowing)
• Electron transfer (Marcus' Theory, reorganization energy and activation energy, superexchange and charge transfer in DNA)
• Proton transfer (double Born-Oppenheimer separation, adiabatic and nonadiabatic, strongly bound protons)

After successful completion of the module, the participants are able to describe elementary processes in molecular systems on the basis of quantum mechanics.

They are able to:

• distinguish different elementary processes and to visualize them in a Jablonski diagram
• describe the structural reorganization during an electronic transition with the displaced oscillator model
• apply Fermi's golden rule to molecular transitions and to formulate the rate expression with the correlation function formalism
• formulate the influence of statistical energy fluctuations on the transfer rate and to explain the connection with the lineshape
• describe elementary models for energy transfer, electron transfer and proton transfer and to apply these to molecular systems.
• interpret optical spectra of molecular dimers and longer aggregates and to analyze their excitonic  structure
• describe the influence of disorder and to explain the appearance of sharp absorption bands
• describe Förster's model for energy transfer and to explain the dependency on distance and spectral overlap
• derive the relation between reorganization energy and activation energy and to explain the dependency of the transfer rate on the free reaction enthalpy according to Marcus
• explain the superexchange mechanism and to apply it to charge transfer in DNA
• compare the length dependency of superexchange and diffusive hopping
• apply the double Born-Oppenheimer separation to molecular systems and to describe the peculiarities of strongly bound protons.

The module "quantum methods for molecular systems" (PH2165) is complementary but not a requirement

The module consists of a lecture and an exercise.

During the lecture the necessary mathematical methods are explained and important theoretical results are derived explicitly. Functional relationships are shown with graphics and computer examples. Theoretical results are compared with experimental data from the literature with the help of computer presentations. After the lecture there is time for discussion.

In the exercises in numerous problem examples the mathematical derivations are discussed in more detail and their application is exercised using selected problem examples and calculations. Thus the students are able to explain and apply the learned knowledge on their own.

A series of interactive applets are introduced in the lecture and serve for individual studies visualizing functional relationships and the  dependency  of the theoretical results on the relevant parameters

Additional notes and literature references are provided for further deepening of the learning content

asynchronous online-lectures and tutorial java programs and extra material, lecture notes, exercises with solutions

• Lecture notes
• P.O.J. Scherer & S.F. Fischer: Theoretical Molecular Biophysics, Springer, (2017)

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:

• explain intramolecular processes with an Jablonski diagram
• apply the double Born-Oppenheimer separation and explain the peculiarities for transfer of strongly bound protons
• apply the model of displaced harmonic oscillators to an optical transition
• discuss the role of the reorganisation energy for electron transfer
• describe the absorption spectrum of a molecular dimer
• explain Förster resonance energy transfer and discuss the important parameters
• explain the relation between reorganization energy and activation energy and discuss Marcus' electron transfer rate