The average bond-length of diatomic molecules in thermodynamical equilibrium depends on the volume
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914717482614784 |
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| author | Echenique-Robba, Pablo |
| author_facet | Echenique-Robba, Pablo |
| contents | In the framework of classical statistical mechanics and assuming the electronic ground-state Born-Oppenheimer approximation, we show in this work that a dependence of the equilibrium bond-length on the available volume is to be expected for a dilute gas of diatomic molecules. In a nutshell, this dependence is controlled by the relation between the potential well depth $D$ (through the factor $e^{-βD}$) and the quotient $L/R$ of the linear size of the container $L$ and the potential well width $R$. Using simplified analytical estimations, we predict that the equilibrium bond-length $\langle ρ\rangle$ is independent of $L$ for a range of volumes which is exponentially large on $βD$. At some point of the $L$ axis, $\langle ρ\rangle$ starts to increase and it eventually diverges, as it is to be expected, when $L \to \infty$, thus describing dissociated atoms. According to our estimations, it is possible that some diatomic molecules, such as halogens, could present volume dependence of their equilibrium bond-lengths for laboratory-size volumes at room temperature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10974 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The average bond-length of diatomic molecules in thermodynamical equilibrium depends on the volume Echenique-Robba, Pablo Chemical Physics In the framework of classical statistical mechanics and assuming the electronic ground-state Born-Oppenheimer approximation, we show in this work that a dependence of the equilibrium bond-length on the available volume is to be expected for a dilute gas of diatomic molecules. In a nutshell, this dependence is controlled by the relation between the potential well depth $D$ (through the factor $e^{-βD}$) and the quotient $L/R$ of the linear size of the container $L$ and the potential well width $R$. Using simplified analytical estimations, we predict that the equilibrium bond-length $\langle ρ\rangle$ is independent of $L$ for a range of volumes which is exponentially large on $βD$. At some point of the $L$ axis, $\langle ρ\rangle$ starts to increase and it eventually diverges, as it is to be expected, when $L \to \infty$, thus describing dissociated atoms. According to our estimations, it is possible that some diatomic molecules, such as halogens, could present volume dependence of their equilibrium bond-lengths for laboratory-size volumes at room temperature. |
| title | The average bond-length of diatomic molecules in thermodynamical equilibrium depends on the volume |
| topic | Chemical Physics |
| url | https://arxiv.org/abs/2403.10974 |