Hund's coupling cases

The Hund's coupling cases describe the different ways of coupling of rail - and spin - angular momentum vectors ( spin-orbit interaction ) within a molecule . They were set up by the physicist Friedrich Hund and are part of the quantum mechanical description of molecules, meaning and a. for molecular spectroscopy .

Of the five coupling cases a) to e), cases a) and b) are particularly relevant.

General

An important difference to atoms is that molecules can exert vibrations and rotations , which have an influence on the energetic state of the molecule. The total angular momentum of a molecule is composed in different ways from the molecular angular momentum of the nuclei as well as the orbital and spin angular momentum vectors and the electrons . ${\displaystyle {\vec {J}}}$ ${\displaystyle {\vec {N}}}$ ${\displaystyle {\vec {L}}}$ ${\displaystyle {\vec {S}}}$

Hund's coupling case a)

Sketch for coupling case a) for a diatomic molecule

Hund's coupling case a) occurs when there is a small interaction between the rotation of the molecule and the movement of the electrons. The orbital and spin angular momentum vectors and the electrons are therefore bound to the molecular axis around which they rotate in rapid precession . The sum of their projections onto the molecular axis ( and ) is called the total electron angular momentum . The total angular momentum , on the other hand, is constant in terms of both magnitude and direction. ${\displaystyle {\overrightarrow {L}}}$ ${\displaystyle {\overrightarrow {S}}}$ ${\displaystyle \Lambda }$ ${\displaystyle \Sigma }$ ${\displaystyle \Omega }$ ${\displaystyle {\overrightarrow {J}}}$

Hund's coupling case b)

Sketch for coupling case b) for a diatomic molecule

In Hund's coupling case b) the spin angular momentum vector is only weakly or not at all bound to the molecular axis. The vectors and add up to a vector around which the molecular axis precedes during rotation. In a more precise description, the spin angular momentum vector of the electrons is added. The result is the total angular momentum vector , which is constant over time, as in the coupling case a). The molecule therefore performs a complicated circular motion consisting of two precessions. ${\displaystyle {\overrightarrow {S}}}$ ${\displaystyle \Lambda }$ ${\displaystyle {\overrightarrow {N}}}$ ${\displaystyle {\overrightarrow {K}}}$ ${\displaystyle {\overrightarrow {K}}}$ ${\displaystyle {\overrightarrow {S}}}$ ${\displaystyle {\overrightarrow {J}}}$

See also

• Hund's rules