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Here we have the experimental enthalpy of melting (fusion) and some models activity coefficient(macroscopic equation of state, free energy calculation, divine intervention ...). note that the activity coefficient depends on the composition, so the composition (solubility) is on the left and right hand side. Thus, we have to solve this iteratively, which is why is is nice for macroscopic models, which takes fractions of seconds, and, not so nice for molecular models which take hours(have not actually done this yet using MD, it is on my list of things to do). I find that a simple secant method is fine when doing it using macroscopic equations of state. Simply updating will unfortunately lead to divergence sometimes.

Option 2

Here we have the experimental enthalpy of melting (fusion) and some models activity coefficient(macroscopic equation of state, free energy calculation, divine intervention ...). note that the activity coefficient depends on the composition, so the composition (solubility) is on the left and right hand side. Thus, we have to solve this iteratively, which is why it is nice for macroscopic models, which takes fractions of seconds, and, not so nice for molecular models which take hours(have not actually done this yet using MD, it is on my list of things to do). I find that a simple secant method is fine when doing it using macroscopic equations of state. Simply updating will unfortunately lead to divergence sometimes.

Option 2:

Another option is to set up slabs of the solid in the solution, and then simply run MD or MC. the solids will slowly dissolve into the solution, and at some appropriate spot in the bulk, you measure the concentration of the solute. This is also not so trivial as it seems, but look to literature for guidance. A good question is "what is the solid (crystal) form of my drug molecule?". The answer is frequently unknown...

Another option is to set up slabs of the solid in the solution, and then simply run MD or MC. the solids will slowly dissolve into the solution, and at some appropriate spot in the bulk, you measure the concentration of the solute. This is also not so trivial as it seems, but look to literature for guidance. A good question is "what is the solid (crystal) form of my drug molecule?". The answer is frequently unknown... Also, does the FF model the crystal solid well? probably not.

$\ln (x_i) = \frac{\Delta H_m}{R} \left(\frac{1}{T_m} - \frac{1}{T} \right) + RT \ln \gamma_i(x_i)$

(note I need to verify this, my memory is hazy and wikipedia is bad at this stuff. I will look up my own code later, it works, so... I trust it more than wikipedia. I may have plus and/or minus signs wrong here).

Another option is to set up slabs of the solid in the solution, and then simply run MD or MC. the solids will slowly dissolve into the solution, and at some appropriate spot in the bulk, you measure the concentration of the solute. This is also not so trivial as it seems, but look to literature for guidance. A good question is... what is the solid (crystal) form of my drug molecule... the answer is frequently unknown...

option 3:

Try to correlate something to experimental results and use this fit to predict solubility. This type of rational design strategy makes me a bit queasy, but, sometimes science doesn't have a quantitative strategy that is computationally feasible, and we have to fall back on parameter fitting... Who knows, maybe there is a good correlation between radius of gyration and free energy, or solubility... you could throw in hydrogen bonding sites into the regression as well, the list of features never ends...

$$\ln (x_i) = \frac{\Delta H_m}{R} \left(\frac{1}{T_m} - \frac{1}{T} \right) + RT \ln \gamma_i(x_i)$$

(note I need to verify this, my memory is hazy and Wikipedia is bad at this stuff. I will look up my own code later, it works, so... I trust it more than Wikipedia. I may have plus and/or minus signs wrong here).

Another option is to set up slabs of the solid in the solution, and then simply run MD or MC. the solids will slowly dissolve into the solution, and at some appropriate spot in the bulk, you measure the concentration of the solute. This is also not so trivial as it seems, but look to literature for guidance. A good question is "what is the solid (crystal) form of my drug molecule?". The answer is frequently unknown...

Option 3:

Try to correlate something to experimental results and use this fit to predict solubility. This type of rational design strategy makes me a bit queasy, but, sometimes science doesn't have a quantitative strategy that is computationally feasible, and we have to fall back on parameter fitting. Who knows, maybe there is a good correlation between radius of gyration and free energy, or solubility. You could throw in hydrogen bonding sites into the regression as well, the list of features never ends...