SUBJECT

Quantum Mechanics of Molecular Vibrations

lecture

Master

Faculty of Science

Chemistry MSc

2

Semester 4

Spring semester

Separation of electronic and nuclear motions. The Born–Oppenheimer and the adiabatic approximations. Separation of vibrational and rotational motions: the Eckart conditions. The 1-D harmonic linear oscillator, its solution with traditional and advanced methods. Matrix elements of harmonic oscillator functions. Anharmonic oscillator in one dimension (perturbation theory). Harmonic vibrational analysis for N-atom molecules. Normal vibrations. The GF method. The SQM method. Vibrational perturbation theory. Van Vleck transformation. Energy formulae. Resonances. Variational solution of the rotational-vibrational problem. Coordinate systems. General form of the kinetic energy operatoring different coordinate systems. Potential energy hypersurfaces and their ab initio determination. Efficient determination of matrix elements. The DVR technique. Diagonalization methods. Normal and local vibrations. Ab initio rotational-vibrational spectroscopy.

Compulsory: 

• Császár Attila: Lecture notes (xerox copy, library of ELTE TTK KI).

Suggested:

• Ira N. Levine: Molecular Spectroscopy, Wiley-Interscience: New York, 1975

• Ira N. Levine: Quantum Chemistry, Wiley-Interscience: New York, 1999