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edited paragraph on solvation free energy calc to improve clarity
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ptmerz authored and orbeckst committed Jun 5, 2024
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Free energy differences are fundamental to understand many different processes at the molecular scale, ranging from the binding of drug molecules to their receptor proteins or nucleic acids through the partitioning of molecules into different solvents or phases to the stability of crystals and biomolecules.
The calculation of such transfer free energies involves constructing two end states where a target molecule interacts with different environments.
For example, in a solvation free energy calculation, at one state (the coupled state) it interacts with a solvent (in the case of hydration free energies, water), and the other where the ligand has no intermolecular interactions (the decoupled state), mimicking the transfer of a ligand at infinite dilution in the solvent at one end of the process and then ligand in the gas phase at the other.
The solvation free energy is then obtained by calculating the free energy difference between these two end states.
To achieve this, it is crucial to ensure sufficient overlap in phase space between the coupled and decoupled states, a condition often challenging to achieve.
For example, in a solvation free energy calculation, in one state (the coupled state) the target molecule interacts with a solvent (in the case of hydration free energies, water), while in the other state (the decoupled state) the ligand has no intermolecular interactions, which mimics the transfer of a ligand from infinite dilution in the solvent to the gas phase.
The solvation free energy is then obtained by calculating the free energy difference between these two end states, but it is crucial to ensure sufficient overlap in phase space between the coupled and decoupled states, a condition often challenging to achieve.

Stratified alchemical free energy calculations have emerged as a de-facto standard approach whereby non-physical intermediate states are introduced to bridge between the physical end states of the process [@Mey2020aa].
In such free energy calculations, overlapping states are created by the introduction of a parameter $\lambda$ that continuously connects the functional form (the Hamiltonian of the system) of the two end-states, resulting in a series of intermediate states each with a different $\lambda$ value between 0 and 1 and with the physically realizable end states at $\lambda=0$ and $\lambda=1$.
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