Multiplicity (chemistry)

Under multiplicity is understood in quantum mechanics that eigenstates are degenerate to an operator, that is, that they are more states with the same eigenvalue.

An example of this is the spin multiplicity, which is often simply called multiplicity. If one considers, for example, the hydrogen atom, then the electron in the ground state of two spin states (or linear combinations of them) are taking. Without an external field, the two states have the same energy and can therefore not be distinguished energetically.

In general, a system with total spin, the spin multiplicity. The multiplicity indicates in how many different spatial directions can adjust the spin vector of a particle with respect to easy axis (for example, in a magnetic field ) ( space quantization ):

This is the " spin magnetic" quantum number.

Multiplicity of atoms and molecules

In systems of a plurality of electrons and / or nuclei of the atomic nuclei is a distinction between the spin multiplicity of the electron and the spin multiplicity.

Multiplicity of the electron spin

One-electron systems

Figuratively one imagines under the spin of an electron often the intrinsic angular momentum ago, created by the "rotation" of an electron around its own axis, this axis to a predetermined direction has only two choices: either parallel or antiparallel. However, this notion is useful only within limits and actually untenable. Formally, the spin momentum is associated with the quantum number. The multiplicity of the one-electron system is so. There is therefore an electronic doublet state.

• For example, a single hydrogen atom H • (So it could be below as an example for a radical with zero paired electrons in the table. )

Many-electron systems

In atoms ( or ions ) with several electrons and molecules must first be determined, the total spin quantum number of the entire electronic system. For an atom with electrons is given by

Wherein the spin quantum number of the i-th electron. Since the individual spins paired electrons do not contribute to the total spin due to the opposite orientation, it is enough to count the unpaired electrons. Your individual spin quantum numbers add up to the total spin quantum number

Meaning: selection rules, intercombination prohibition

The numerical value of the multiplicity is expressed in the term superscript symbols on the left, which are often used to characterize the quantum states of atoms and molecules.

• For example, for hydrogen atoms (H ) in the ground state term symbol is the 2S1 / 2 (multiplicity 2).

Multiplicity plays an important role for the selection rules in spectroscopy. For electric dipole transitions take place particularly well if the multiplicity is maintained ( allowed transition, such as fluorescence from the first excited singlet state to the singlet ground state).

In contrast, processes apply where the multiplicity changes ( intercombination ), according to the usual in spectroscopy parlance as forbidden ( intercombination prohibition ). More specifically expressed the fact that they usually ( i.e. statistically rare) only to a small extent or " slow" to take place, such as in the phosphorescence (transition from the lowest excited triplet state to the singlet ground state ).

Multiplicity of the nuclear spins

The total spin of the nuclei in a molecule is composed of the nuclear spins of the individual nuclei. Unlike the electron, however, the nuclear spin of the nuclei is not always the same but depends on the composition of the particular core. Here too, then gives the multiplicity according to the formula.