diff --git a/_lessons/Introduction.md b/_lessons/Introduction.md index 51fa675..8f387dd 100644 --- a/_lessons/Introduction.md +++ b/_lessons/Introduction.md @@ -69,7 +69,7 @@ There are a number of key notes we can learn from the definition of free energy - **Only free energy __differences__ are ever calculated** There is never a calculation where absolute free energies are needed (and rarely can they be calculated at all) as all of the biological or thermodynamical quantities of interest are based on a free energy difference. As such, there must always be a minimum of two defined thermodynamic states. Even ''absolute'' free energies of binding are still free energy differences between two states: the ligand restricted to the binding site, and the ligand free to explore all other configurations. - **Free energy differences between states at different temperatures are usually not what you want to be calculating** for problems of interest. If it did, you would get $\Delta A_{ij} = -k_B T_j \ln Q_j + k_B T_i \ln Q_i$, which is no longer a ratio calculation and not needed for biological systems of interest. Temperature dependence on free energy is more likely to be "what is $\Delta A_{ij}$ at two different temperatures?" -- **There are two potentially different phase space volumes.** $\Gamma_i$ and $\Gamma_j$ are often the same, but they are not required to be. The methods presented here almost always assumes that the two phase spaces overlap. However, when the spaces do not overlap, these methods break down and it is difficult to identify this problem without in depth knowledge of your system. Consider the example of a hard sphere solute with radius $\sigma$ at state $i$ and a Lennard Jones repulsion/dispersion potential, with the same $\sigma$ at state $j$. Since $\Gamma _i$ will not have molecules at a distance less than $\sigma$, but $\Gamma_j$ will, the two phase spaces are not the same and these methods will either break down or return very error-prone results. - The degree to which the phase spaces are shared is called the "phase space overlap". Efficient free energy calculations require significant phase space overlap. There are [[Intermediate_States | a number of strategies to address]] lack of overlap between target spaces, but determining the best way for any given situation is still a research question. +- **There are two potentially different phase space volumes.** $\Gamma_i$ and $\Gamma_j$ are often the same, but they are not required to be. The methods presented here almost always assumes that the two phase spaces overlap. However, when the spaces do not overlap, these methods break down and it is difficult to identify this problem without in depth knowledge of your system. Consider the example of a hard sphere solute with radius $\sigma$ at state $i$ and a Lennard Jones repulsion/dispersion potential, with the same $\sigma$ at state $j$. Since $\Gamma_i$ will not have molecules at a distance less than $\sigma$, but $\Gamma_j$ will, the two phase spaces are not the same and these methods will either break down or return very error-prone results. + The degree to which the phase spaces are shared is called the "phase space overlap". Efficient free energy calculations require significant phase space overlap. There are (a number of strategies)[Intermediate-States] to address the lack of overlap between target spaces, but determining the best way for any given situation is still a research question. - It should also be noted that "near zero probability" and "always zero probability" are two distinct things when considering phase space. So long as there is a chance for an observation to be made, no matter how small, it is considered part of the phase space (though long simulations might be needed to sample this overlap).