Zero-Range Potentials for Molecular Systems. Bound States
The determination of the bound-state energy levels of an electron moving in the potential field of a complicated molecule is a typical problem in quantum chemistry. The resulting field is a superposition of several spherically symmetrical potentials centered on the nuclei of the molecule. The solution of such problems with real potentials encounters great numerical difficulties. Therefore it is important to see whether simpler models can be developed to give a qualitatively correct description of the molecules. In this chapter, we shall consider a superposition of several ZRPs forming a many-center potential field. The corresponding Schrödinger equation for an arbitrary number of force centers admits an analytical solution. This model can be applied to study quantum-mechanically the motion of outer electrons in negative molecular ions. With a suitable choice of parameters, it can also be applied to the inner electrons of these molecular systems.
KeywordsBranch Point Potential Energy Curve Schrodinger Equation Force Center Internuclear Separation
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