# Modul M.Che.1311 (WiSe 2023/24, 6Cr)

### Vibrational Spectroscopy and Intermolecular Dynamics

### (Schwingungsspektroskopie und zwischenmolekulare Dynamik)

The lecture (3h/week, Fridays, 8:15-11:00 AM, starting 27.10.23) in MN27 (unless forced to Stud.IP/meetings for some reason), is one among currently 6 choices for more specialized Physical Chemistry lectures in the Chemistry Master's program. In the winter term 2023/24 it will be held in English to allow for participation in the Master's program despite a possibly limited command of German. Active participation in the accompanying tutorial (tentatively Mondays, 2:15-4:00 PM or Wednesdays 4:15-6:00 PM, discussing homework exercises) is urgently recommended, to optimize performance in the final written exam (180 min, planned for 09.02.24, 8AM and in spring 2024). In addition, weekly voluntary multiple choice tests (Stud.IP) to check your level of understanding are offered. The next occasion to attend this lecture is planned for WiSe 2024/25 (then mostly in German). See Stud.IP for further information.

A brief meeting on organizational details will be offered on 27.10.23, 8:00 AM

Lecture program (incl. date):

**Vibrating diatomics (27.10.)**

Introduction into the lecture topic, molecular vibration, classical-quantum mechanical correspondence, harmonic oscillator, Morse oscillator, wavefunctions, energy levels, infrared spectrum, rotational constants, mechanical and electrical anharmonicity, matrix elements, overtone intensity**Molecular symmetry I (03.11.)**

symmetry operation, symmetry element, symmetry group, group properties, point groups, symbols, proper rotation, reflection, inversion, improper rotation, abelian groups with at most two-fold axes, examples, subgroups, classification scheme, other symmetry groups and their classification**Molecular symmetry II (10.11.)**

symmetry properties of molecular properties, characters, example C_{2v}, character table, irreducible representations, Mulliken symbols, coordinate systems, symmetrization, further abelian groups and their character tables, subgroups, symmetry number, chirality, dipole moments, transition dipole moments, harmonic oscillator**Molecular symmetry III (17.11.)**

molecular vibrations exemplified for water, matrix representation of atomic displacements, trace, reducible representations and their reduction, translational, rotational and vibrational degrees of freedom, normal modes, symmetry reduction, selection rules, Raman, IR, C_{3v}, degenerate representations, molecular symmetry groups**Normal modes (24.11. held by Dr. Nils Lüttschwager)**

Hamilton function, mass-weighted displacement coordinates, similarity transform, normal coordinates, degeneracy, stretching modes in CO_{2}, matrix notation, symmetric and antisymmetric stretching mode, kinematic coupling, valence force constants, functional group vibrations, fingerprint vibrations**Anharmonic effects (01.12.)**

Anharmonicity constants in polyatomic molecules, Fermi resonance, coupling matrix elements, solution of the 2x2 problem, limiting cases, wavefunction character, example CO_{2}, vibrational terms, variational calculations, potential hypersurfaces and coordinate choice, state of the art, diffusion quantum Monte Carlo, concept, derivation based on the time-dependent Schrödinger equation, analogy to a transport equation, double minimum potential, tunneling splitting and period, ring puckering, torsion potential**Experimental techniques in vibrational spectroscopy (08.12.)**

Application range, historical evolution, IR, Raman, neutron scattering, fluorescence, detectors, photovoltaic and thermal detectors, detector noise, cross section, Beer-Lambert law, light sources, thermal emitters, tunable lasers, optical materials, FTIR spectrometer**Intermolecular interactions (15.12.)**

Electrostatic interactions, multipole expansion, dipole, quadrupole, potential energy, dipole-charge, dipole-dipole, thermal averaging, dipole-quadrupole, quadrupole-quadrupole, induction, polarisability, dispersion interactions**Structures of moleclar clusters (22.12.)**

Pauli repulsion, supermolecule approach, anisotropy in the bonding region, Ar-HX examples, HX-HX examples, water dimer, quadrupolar molecules, structure determination methods, hydrogen bonds, energy and structure contributions, structure, relevance, directionality, oligomers, solid state structures, rings and cages, history**Potential energy hypersurfaces and vibrational dynamics of molecular clusters (12.01.)**

Lennard-Jones potential, well depth estimates, van der Waals radii, mixing rules, Buckingham potential, partial charges, Stockmayer potential, empirical force fields for molecular mechanics and biochemistry, refined model potentials, pair approximation, three-body forces, induction, Pauli repulsion, Axilrod-Teller term, importance of many-body forces, zero-point vibration, He dimer, intermolecular vibrations, intramolecular vibrational shifts, the case of t-butyl alcohol, intensity enhancement, predissociation, Franck-Condon transitions, down shift and bond strengthening, OH band broadening in solution, tunneling splitting, energy flow after excitation**Experimental methods and examples for cluster generation and cluster spectroscopy (19.01.)**

Aggregation, condensation, natural molecular clusters, aggregates in solution, matrix isolation, enclosive flow cooling, supersonic jet expansion, IR-spectroscopy, absorption spectroscopy, cavity ring-down spectroscopy, size selection by scattering, water clusters, carboxylic acid clusters, ionic clusters, clusters in clusters**Miscellaneous (26.01.+02.02.)**

UV/IR techniques, fs-spectroscopy in solution, exciton coupling in water, anharmonic calculations, vibrational microscopy, molecular sociology, oscillator model of dispersion, chirality recognition, evaluation, good scientific practice**Exam (1st option, 09.02.24)****Exam (2nd option, 04.03.24)**

previous examples

#### Recommended reading

A good general textbook of Physical Chemistry (Berry/Rice/Ross, McQuarrie/Simon, Atkins/dePaula, Wedler, Alberty/Silbey, Moore/Hummel, ...) forms a solid base. Consider the English original, if available (price, topicality).

Complementary reading for selected chapters:

1.+7.: see *Literatur zur
Molekülspektroskopie*.

2.-4.: Zachmann *Mathematik für Chemiker* (only older editions), Cotton *Chemical
Applications of Group Theory* and Vincent *Molecular Symmetry and Group
Theory* (simple) and Lorenz et al. *Molekülsymmetrie und Spektroskopie*
(German) and Hamermesh *Group Theory and Its Application to
Physical Problems* (demanding)

5.+6.: Wilson, Decius, Cross *Molecular Vibrations*

7.-11.: Kleinermanns (Hrsg.) *Bergmann/Schaefer Experimentalphysik*,
Bd. 5, *Gase, Nanosysteme, Flüssigkeiten*

8.+10.: Stone *The Theory of Intermolecular Forces* and Jeffrey
*An Introduction to Hydrogen Bonding*

11.: Scoles (Hrsg.) *Atomic and Molecular Beam Methods*

Some of the listed books are available as ebooks via SUB:

- Hermann Haken, Hans Christoph Wolf, Molekülphysik und Quantenchemie
- Morton Hamermesh, Group Theory and Its Application to Physical Problems
- John Michael Hollas, Modern Spectroscopy
- Ingo-Peter Lorenz, Norbert Kuhn, Stefan Berger und Dines Christen, Molekülsymmetrie und Spektroskopie
- Walter John Moore, Dieter O. Hummel, Physikalische Chemie
- Anthony Stone, The Theory of Intermolecular Forces
- Gerd Wedler und Hans-Joachim Freund, Lehr- und Arbeitsbuch Physikalische Chemie
- E. Bright Wilson, J. C. Decius, Paul C. Cross, Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra

(To access the ebooks, login via eduroam or establish a VPN-connection to the university network.)