Molecules with two electronic energy levels : deviation from the canonical distribution for N identical and independent sets of two molecules linked by a chemical bond.
Résumé
A spin-conversion molecule is organised around an iron ion $Fe^{+2}$. This
ion has two quantum energy levels : a low spin (LS) ground level, $S=0$, and
a high spin (HS) excited level, $S=2$ , where $S$ is the total spin of the $%
3d$ electrons.\ We call $\Delta $ the distance in energy of the two levels.
This result is described by introducing a fictitious spin $\widehat{\sigma }$
which has two eigenvalues $\pm 1$. For a set of two molecules we introduce
the sum $\widehat{\sigma }_{1}+\widehat{\sigma }_{2}$ of two fictitious
spins which has the eigen values $\pm 2$ and $0$. The vibrations inside each
molecule and the vibrations between the two molecules are taken into
account. These vibrations are independent of each other but their frequency
depends on the electronic states of the two molecules. For the following,
each molecule is designated by atom and the set of two molecules is
designated by molecule.
From the statistical study, its appears at equilibrium, for fixed $T$ and $%
\Delta /2$, three thermodynamic states $\left( -2\right) $, $\left( 0\right)
$ and $\left( 2\right) $ with occupation probabilities $P\left( -2\right) $,
$P\left( 0\right) $ and $P\left( 2\right) $, respectively. For each state we
can calculate its Gibbs potential, its entropy and its enthalpy. The
intensive parameters are the temperature $T$ and $\Delta /2$.
For an ensemble of $N$ identical molecules, there are at the (Boltzmann)
equilibrium $NP\left( -2\right) $ molecules in the state $\left( -2\right) $%
, $NP\left( 0\right) $ in the state $\left( 0\right) $ and $NP\left(
2\right) $ in the state $\left( 2\right) $. But, as the Gibbs potentials of
the three states are not equal, this canonical distribution is not stable.
Then, due to random exchanges of heat between the thermostat and the
molecules, the molecules will all go to the the state with the lowest Gibbs
potential.
Domaines
Physique [physics]
Origine : Fichiers produits par l'(les) auteur(s)
licence : CC BY - Paternité
licence : CC BY - Paternité