Modul M.Che.1311 (WS 2013/14, 6 Cr)

Schwingungsspektroskopie und zwischenmolekulare Dynamik

(Vibrational Spectroscopy and Intermolecular Dynamics)

Die Vorlesung (3 SWS, Freitags, 08:15 - 11:00 Uhr, AC-Werkstattgebäude, HS III, MN29, Beginn 25.10.13) ist eine von derzeit 5 Wahlpflichtvorlesungen der Physikalischen Chemie (Elektronische Spektroskopie und Reaktionsdynamik, Schwingungsspektroskopie und zwischenmolekulare Dynamik, Physikalische Chemie der kondensierten Materie, Biophysikalische Chemie, Chemical Dynamics at Surfaces) im Master-Studiengang Chemie (alter Masterstudiengang: Teil von M.Che.1302). Die aktive Teilnahme an der parallel angebotenen Übungsstunde (dort werden selbständig bearbeitete Hausaufgaben vorgerechnet und diskutiert) wird dringend empfohlen, um an der Abschlussklausur (180 min, 07.02.2014 und 17.04.2014) erfolgreich teilzunehmen. Zusätzlich werden bei ausreichender Resonanz eine wöchentliche Fragestunde und ein anonymer Multiple Choice Test (Stud.IP) angeboten.

Die Vorlesung wird diesmal von Dr. Alexandra Domanskaya in englischer/begrenzter deutscher Sprache angeboten. Weitere Informationen zur Vorlesung finden sich im Stud.IP. Das nächste Angebot dieser spezifischen Wahlpflichtvorlesung ist für das WS 2014/15 geplant, dann voraussichtlich überwiegend in deutscher Sprache.

Vorläufiges Vorlesungsprogramm (incl. Datum):

  1. General concepts: Why are “molecular vibrations” and “molecular spectroscopy” often used as synonyms? (25.10.)
    Introduction to the topic of the course. Structure of the course. Harmonic oscillator, frequency interval of molecular vibrations, force constants. Interaction of electromagnetic radiation with molecules. Einstein coefficients. Multipolar expansion, electromagnetic radiation of an oscillating dipole. Polarizability, induced dipole. 3 levels of spectroscopy: frequencies, intensities and profiles. Principal methods: absorption and scattering of light. Transition moments, relation of Einstein coefficients to transition moments and observables. Absorption line strengths, scattering intensities. Lineshapes: natural, Doppler and pressure broadening.

    2. I. Molecules all alone
  2. Diatomic molecules - simple vibrating systems. (01.11)
    Harmonic approach. Vibration-rotational spectrum: rotational constants, selection rules, band formation, nomenclature. Matrix elements. Intensity distribution. Linear dipole moment function. Double harmonic approximation. More realistic model: Morse potential (extension: Dunham potential). Wavefunctions. Anharmonicity, mechanical and electrical. Influence of the anharmonicity on the spectrum. Frequency analysis, Fortrat diagram. Non-linear dipole moment function. Overtones. Vibration-rotation coupling, centrifugal distortions, Hermann-Wallis coefficients.
  3. Step further: polyatomic molecules. (08.11)
    Classical approach - vibrational problem from Newtonian laws, secular equation, vibrational degrees of freedom, modes of vibration, normal modes, Cartesian/mass-weighted or normal coordinates. Quantum vibrational problem in the harmonic approximation, nomenclature of energy levels, degeneracy. Molecule’s vibrational ID: specific fingerprint and general features.
  4. Ease the math: symmetry and polyatomic molecules-1. (15.11)
    Introduction: simple example of the influence of molecular symmetry on the transition dipole moment. Concenpts of group theory. 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, subgroups, classification scheme, other symmetry groups and their classification, symmetry number. First application: existence of a permanent dipole moment and chirality from the symmetry group.
  5. Symmetry and polyatomic molecules-2. (22.11)
    Point group character tables. Deriving the character table for the C2v group. Irreducible representations, Mulliken symbols. Symmetry of translational, rotational and vibrational motion of the H2O molecule. Matrix representation of atomic displacements. Reducible representations and their reduction. Application: number of vibrational modes, symmetry of vibrational wavefunctions, vibrational selection rules for IR/Raman transitions.
  6. Symmetry and polyatomic molecules-3. (29.11)
    Further abelian groups and their character tables: worked example for the C2h group. Complementary selection rules. Non-abelian groups, degenerate representations. Infinite groups. Influence of the symmetry on the vibrational band profile. Symmetric and spherical top molecules. Molecular symmetry groups.
  7. Anharmonic effects. (06.12)
    Anharmonicity and coupling constants in polyatomic molecules. Fermi-resonance, perturbation theory, solving 2×2 case, example for the CO2 molecule. Vibrations of molecules with several equilibrium positions, tunneling. Molecules with internal rotation, torsion potential. Coriolis interaction.
  8. Experimental methods. (13.12)
    Principal scheme of the absorption/Raman experiment. Parameters: resolution, light throughput. Dispersive vs. Fourier transform spectrometers. Dispersive elements: prism, grating. Fourier transform spectrometer, interferogram, resolution in FTIR experiments, instrument function, apodisation function, folding, FTIR advantages. Overview of common commercial optical components.

    9. II. When molecules meet
  9. Intermolecular interactions. (20.12)
    Electrostatic interaction, potential energy, multipole expansion, charge, dipole, quadrupole. Dipole – dipole, dipole – quadrupole, quadrupole – quadrupole interaction, thermal averaging. Polarisability tensor, dipole – induced dipole interaction, dispersion interaction.
  10. Geometry of a molecular complex – equilibrium between repulsion and attraction. (10.01)
    Pauli (exchange) repulsion, anisotropy in the bonding region, examples. Methods of structure determination. Hydrogen bonding, contribution to the binding energy and geometry.
  11. Potential energy hypersurface and vibrational dynamics of molecular aggregates. Spectroscopic markers. (17.01)
    Born-Meyer potential: induced spectra of colliding unlike atoms. Lennard-Jones, Kihara potentials, van der Waals-radii, combining rules. Buckingham and Stockmayer potentials. Force fields. Binary approximation, validity and limitations. Many-body interaction. Intermolecular vibrations. Intensity enhancement, red-shift and bond strengthening of intramolecular vibrations. Energy distribution upon excitation.
  12. Experimental methods and examples of cluster formation and cluster spectroscopy. (24.01)
    Cluster formation, condensation, natural clusters, clustering in solution. Matrix isolation (shortly), cryospectroscopy, supersonic jet. Cavity ring-down method, Raman and IR microscopy. Examples (jet-mapping, alcohol-ketone demixing, water/alcohol clusters, hydrogen halides complexes).
  13. Matrix isolation method. (31.01)
    Main features, hosts, accessible temperatures, advantages/disadvantages. Overview of possible applications: exotic molecules and radicals, high-energy conformers, complexation and dimerization, spectroscopic studies of chemical reactions, kinetic measurements of tunneling processes.
    Evaluation.
  14. Klausur (07.02, 8:00-11:00 Uhr)

    Frühere Klausuraufgaben:
    Klausur vom 17.7.2012 (PDF-Datei)
    Klausur vom 25.9.2012 (PDF-Datei)
    Klausur vom 12.7.2011 (PDF-Datei)
    Klausur vom 05.02.2010 (PDF-Datei)
    Klausur vom 01.04.2008 (PDF-Datei)

Literaturempfehlung

Ein gutes allgemeines Lehrbuch der Physikalischen Chemie (Berry/Rice/Ross, McQuarrie/Simon, Atkins, Wedler, Alberty/Silbey, Moore/Hummel, ...) reicht mehrheitlich aus. Bei angelsächsischen Autoren ist in der Regel die englischsprachige Originalausgabe zu empfehlen (Preis, Aktualität, wichtige Sprachübung).

Ergänzende Literatur zu einzelnen Kapiteln:

1.+8.: Siehe Literatur zu PC 2.

W. Demtröder, Atoms, Molecules and Photons, Springer, Berlin, ISBN-13 978-3-540-20631-6

3-7.: E. B. Wilson, Jr., J. C. Decius, P. C. Cross, Molecular vibrations, Dover publications

4.: http://symmetry.otterbein.edu/index.html / - good visualisation of symmetry elements and training of symmetry recognition.

4-6.: Zachmann Mathematik für Chemiker, Cotton Chemical Applications of Group Theory und Vincent Molecular Symmetry and Group Theory (einfach),
siehe auch http://symmetry.jacobs-university.de/

8.: Guide for infrared spectroscopy, Bruker - small and handy PDF, which helps to orient in the optical materials.

9-10.: Stone, The Theory of Intermolecular Forces und Jeffrey, An Introduction to Hydrogen Bonding

10.: C. Sandorfy, Kap. 13 in The Hydrogen Bond, Band 2, Hrsg. P. Schuster, G. Zundel, C. Sandorfy, 1976, North-Holland

12.: Scoles (Hrsg.), Atomic and Molecular Beam Methods; Martin A. Suhm, Hydrogen Bond Dynamics in Alcohol Clusters, Adv. Chem. Phys. 142 (2009) 1-57, doi:10.1002/9780470475935.ch1

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