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Pré-Publication, Document De Travail Année : 2023

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.

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Dates et versions

hal-03945906 , version 1 (18-01-2023)
hal-03945906 , version 2 (05-03-2023)
hal-03945906 , version 3 (21-05-2023)
hal-03945906 , version 4 (13-07-2023)

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  • HAL Id : hal-03945906 , version 3

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J.A. Nasser. 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.. 2022. ⟨hal-03945906v3⟩
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