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  1. Chemical State

    Linked via "Boltzmann distribution"

    Thermodynamics of State Population
    In bulk matter, the chemical state is not singular but represented by a statistical ensemble, governed by the partition function, $Z$. The probability of a system being found in state $n$ at a given temperature $T$ is given by the Boltzmann distribution:
    $$

  2. Molecular Structure

    Linked via "Boltzmann distribution"

    The structure of a molecule is rarely static, particularly in solution. Molecules exist as an ensemble of rapidly interconverting conformers, each corresponding to a local minimum on the PES.
    The energy difference ($\Delta E$) between two conformers, $A$ and $B$, determines their relative populations at a given temperature ($T$) via the Boltzmann distribution:
    $$\frac{[B]}{[A]} = \exp \left(-\frac{EB - EA}{k_{\text{B}} T}\right)$$
    where $k_{\text{B}}$ is the [Boltzmann constant](/entries/bo…