Morse potential
The Morse potential is a term from molecular physics . The 1929 by American physicist Philip McCord Morse proposed context describes the course of the electronic potential of a diatomic molecule as a function of core bond distance by an exponential approximation:
With
- the (spectroscopic) dissociation energy
- the core distance with the lowest potential energy and
- a constant (sometimes referred to as "stiffness of potential")
These quantities are characteristic of the molecule under consideration.
Since one usually defines the potential at infinity as zero:
the Morse potential is often given in the alternative form:
This shifts the zero point potential . This shift enables the definition of a cutoff radius from which the potential is no longer taken into account.
The Schrödinger equation can be solved analytically with the Morse code. This is how the vibration energies can be calculated:
With
- the Planck's quantum of action
- the vibration quantum number
- the frequency that is linked to the constant of the Morse potential via the particle mass
Nowadays, the RKR potential (RKR stands for Ragnar Rydberg , Oskar Klein and Lloyd Rees ) or the Lennard-Jones potential are used to calculate vibration energies .
literature
- Wolfgang Demtröder: Molecular Physics: Theoretical Foundations and Experimental Methods . Oldenbourg Wissenschaftsverlag, 2003, ISBN 978-3-486-24974-3 , p. 93-94 .
- Ludwig Bergmann, Clemens Schaefer, Wilhelm Raith, with contributions from H. Kleinpoppen , M. Fink, N. Risch: Components of matter: Atoms, molecules, atomic nuclei, elementary particles . Walter de Gruyter, 2003, ISBN 978-3-11-016800-6 , p. 460-462 .
- Gerd Otter, Raimund Honecker: Atoms - Molecules - Cores: Molecular and Nuclear Physics . Vieweg + Teubner, 1996, ISBN 978-3-519-03220-5 , pp. 152-154 .
Individual evidence
- ^ Philip M. Morse: Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels . In: Physical Review . tape 34 , no. 1 , June 1, 1929, p. 57 , doi : 10.1103 / PhysRev.34.57 .
- ^ Ingolf V. Hertel, C.-P. Schulz: Atoms, Molecules and Optical Physics 2: Molecules and Photon Spectroscopy and Scattering Physics . Springer, 2011, ISBN 978-3-642-11972-9 , pp. 13 .